Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind type parameter. More...

Detailed Description

Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type complex or real of arbitrary kind type parameter.

See the documentation of setFFTR for more details.

Parameters

[in]

data

: The input contiguous vector of arbitrary size of,

type complex of kind any supported by the processor (e.g., CK, CK32, CK64, or CK128),
type real of kind any supported by the processor (e.g., RK, RK32, RK64, or RK128),

containing the periodic sequence whose FFT is to be computed.

Returns: fft : The output vector of the same type, kind, and size as the input data, containing the FFT result.

Possible calling interfaces ⛓

: use pm_fftpack, only: getFFTR

fft = getFFTR(data(:))

pm_fftpack::getFFTR
Generate and return the Reverse (unnormalized) Fourier Transform of a periodic sequence of type compl...
Definition: pm_fftpack.F90:1156

pm_fftpack
This module contains procedures and generic interfaces for computing the Discrete Fourier Transform o...
Definition: pm_fftpack.F90:205

Remarks: The procedures under discussion are impure.

Note: This functional generic interface is simply a more flexible but slower wrapper around the subroutine generic interface setFFTR.
As such, this functional interface can be significantly slower than the corresponding subroutine interface.

See also: getFFTF
getFFTR
getFFTI
setFFTF
setFFTR
setFFTI

Example usage ⛓

: 1program example

2

3 use pm_kind, only: SK, IK, LK

4 use pm_io, only: display_type

5 use pm_fftpack, only: getfactorFFT

6 use pm_fftpack, only: getFFTF, getFFTR

7 use pm_distUnif, only: getUnifRand

8 use pm_mathCompare, only: isClose

9 use pm_err, only: setAsserted

10

11 implicit none

12

13 integer(IK) :: i

14 integer(IK) :: lenData

15 type(display_type) :: disp

16 disp = display_type(file = "main.out.F90")

17

18 do i = 1, 5

19 block

20 use pm_kind, only: TKG => CKS

21 real(TKG) :: reltol

22 complex(TKG), allocatable :: data(:), adat(:)

23 call disp%show("lenData = getUnifRand(5, 100)")

24 lenData = getUnifRand(5, 100)

25 call disp%show("lenData")

26 call disp%show( lenData )

27 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

28 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

29 call disp%show("data")

30 call disp%show( data )

31 call disp%skip()

32 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

33 adat = getFFTR(getFFTF(data)) / size(data)

34 call disp%show("adat")

35 call disp%show( adat )

36 call disp%show("reltol = sqrt(epsilon(1._TKG))")

37 reltol = sqrt(epsilon(1._TKG))

38 call disp%show("reltol")

39 call disp%show( reltol )

40 call disp%show("isClose(data, adat, reltol = reltol)")

41 call disp%show( isClose(data, adat, reltol = reltol) )

42 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

43 call setAsserted(all(isClose(data, adat, reltol = reltol)))

44 call disp%skip()

45 end block

46

47 block

48 use pm_kind, only: TKG => CKD

49 real(TKG) :: reltol

50 complex(TKG), allocatable :: data(:), adat(:)

51 call disp%show("lenData = getUnifRand(5, 100)")

52 lenData = getUnifRand(5, 100)

53 call disp%show("lenData")

54 call disp%show( lenData )

55 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

56 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

57 call disp%show("data")

58 call disp%show( data )

59 call disp%skip()

60 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

61 adat = getFFTR(getFFTF(data)) / size(data)

62 call disp%show("adat")

63 call disp%show( adat )

64 call disp%show("reltol = sqrt(epsilon(1._TKG))")

65 reltol = sqrt(epsilon(1._TKG))

66 call disp%show("reltol")

67 call disp%show( reltol )

68 call disp%show("isClose(data, adat, reltol = reltol)")

69 call disp%show( isClose(data, adat, reltol = reltol) )

70 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

71 call setAsserted(all(isClose(data, adat, reltol = reltol)))

72 call disp%skip()

73 end block

74

75 block

76 use pm_kind, only: TKG => CKH

77 real(TKG) :: reltol

78 complex(TKG), allocatable :: data(:), adat(:)

79 call disp%show("lenData = getUnifRand(5, 100)")

80 lenData = getUnifRand(5, 100)

81 call disp%show("lenData")

82 call disp%show( lenData )

83 call disp%show("data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)")

84 data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

85 call disp%show("data")

86 call disp%show( data )

87 call disp%skip()

88 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

89 adat = getFFTR(getFFTF(data)) / size(data)

90 call disp%show("adat")

91 call disp%show( adat )

92 call disp%show("reltol = sqrt(epsilon(1._TKG))")

93 reltol = sqrt(epsilon(1._TKG))

94 call disp%show("reltol")

95 call disp%show( reltol )

96 call disp%show("isClose(data, adat, reltol = reltol)")

97 call disp%show( isClose(data, adat, reltol = reltol) )

98 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

99 call setAsserted(all(isClose(data, adat, reltol = reltol)))

100 call disp%skip()

101 end block

102

103 block

104 use pm_kind, only: TKG => RKS

105 real(TKG) :: reltol

106 real(TKG), allocatable :: data(:), adat(:)

107 call disp%show("lenData = getUnifRand(5, 100)")

108 lenData = getUnifRand(5, 100)

109 call disp%show("lenData")

110 call disp%show( lenData )

111 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

112 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

113 call disp%show("data")

114 call disp%show( data )

115 call disp%skip()

116 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

117 adat = getFFTR(getFFTF(data)) / size(data)

118 call disp%show("adat")

119 call disp%show( adat )

120 call disp%show("reltol = sqrt(epsilon(1._TKG))")

121 reltol = sqrt(epsilon(1._TKG))

122 call disp%show("reltol")

123 call disp%show( reltol )

124 call disp%show("isClose(data, adat, reltol = reltol)")

125 call disp%show( isClose(data, adat, reltol = reltol) )

126 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

127 call setAsserted(all(isClose(data, adat, reltol = reltol)))

128 call disp%skip()

129 end block

130

131 block

132 use pm_kind, only: TKG => RKD

133 real(TKG) :: reltol

134 real(TKG), allocatable :: data(:), adat(:)

135 call disp%show("lenData = getUnifRand(5, 100)")

136 lenData = getUnifRand(5, 100)

137 call disp%show("lenData")

138 call disp%show( lenData )

139 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

140 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

141 call disp%show("data")

142 call disp%show( data )

143 call disp%skip()

144 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

145 adat = getFFTR(getFFTF(data)) / size(data)

146 call disp%show("adat")

147 call disp%show( adat )

148 call disp%show("reltol = sqrt(epsilon(1._TKG))")

149 reltol = sqrt(epsilon(1._TKG))

150 call disp%show("reltol")

151 call disp%show( reltol )

152 call disp%show("isClose(data, adat, reltol = reltol)")

153 call disp%show( isClose(data, adat, reltol = reltol) )

154 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

155 call setAsserted(all(isClose(data, adat, reltol = reltol)))

156 call disp%skip()

157 end block

158

159 block

160 use pm_kind, only: TKG => RKH

161 real(TKG) :: reltol

162 real(TKG), allocatable :: data(:), adat(:)

163 call disp%show("lenData = getUnifRand(5, 100)")

164 lenData = getUnifRand(5, 100)

165 call disp%show("lenData")

166 call disp%show( lenData )

167 call disp%show("data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)")

168 data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

169 call disp%show("data")

170 call disp%show( data )

171 call disp%skip()

172 call disp%show("adat = getFFTR(getFFTF(data)) / size(data)")

173 adat = getFFTR(getFFTF(data)) / size(data)

174 call disp%show("adat")

175 call disp%show( adat )

176 call disp%show("reltol = sqrt(epsilon(1._TKG))")

177 reltol = sqrt(epsilon(1._TKG))

178 call disp%show("reltol")

179 call disp%show( reltol )

180 call disp%show("isClose(data, adat, reltol = reltol)")

181 call disp%show( isClose(data, adat, reltol = reltol) )

182 call disp%show("call setAsserted(all(isClose(data, adat, reltol = reltol)))")

183 call setAsserted(all(isClose(data, adat, reltol = reltol)))

184 call disp%skip()

185 end block

186 end do

187

188end program example

pm_distUnif::getUnifRand
Generate and return a scalar or a contiguous array of rank 1 of length s1 of randomly uniformly distr...
Definition: pm_distUnif.F90:4150

pm_err::setAsserted
Verify the input assertion holds and if it does not, print the (optional) input message on stdout and...
Definition: pm_err.F90:735

pm_err::show
Generate and return an object of type stop_type with the user-specified input attributes.
Definition: pm_err.F90:1618

pm_fftpack::getFFTF
Generate and return the Forward Fourier Transform (a.k.a. Fourier Analysis) of a periodic sequence of...
Definition: pm_fftpack.F90:746

pm_io::skip
This is a generic method of the derived type display_type with pass attribute.
Definition: pm_io.F90:11508

pm_mathCompare::isClose
Generate and return .true. if the two input values are sufficiently close to each other within the sp...
Definition: pm_mathCompare.F90:535

pm_distUnif
This module contains classes and procedures for computing various statistical quantities related to t...
Definition: pm_distUnif.F90:274

pm_err
This module contains classes and procedures for reporting and handling errors.
Definition: pm_err.F90:52

pm_io
This module contains classes and procedures for input/output (IO) or generic display operations on st...
Definition: pm_io.F90:252

pm_io::disp
type(display_type) disp
This is a scalar module variable an object of type display_type for general display.
Definition: pm_io.F90:11393

pm_kind
This module defines the relevant Fortran kind type-parameters frequently used in the ParaMonte librar...
Definition: pm_kind.F90:268

pm_kind::LK
integer, parameter LK
The default logical kind in the ParaMonte library: kind(.true.) in Fortran, kind(....
Definition: pm_kind.F90:541

pm_kind::CKH
integer, parameter CKH
The scalar integer constant of intrinsic default kind, representing the highest-precision complex kin...
Definition: pm_kind.F90:843

pm_kind::CKS
integer, parameter CKS
The single-precision complex kind in Fortran mode. On most platforms, this is a 32-bit real kind.
Definition: pm_kind.F90:570

pm_kind::IK
integer, parameter IK
The default integer kind in the ParaMonte library: int32 in Fortran, c_int32_t in C-Fortran Interoper...
Definition: pm_kind.F90:540

pm_kind::CKD
integer, parameter CKD
The double precision complex kind in Fortran mode. On most platforms, this is a 64-bit real kind.
Definition: pm_kind.F90:571

pm_kind::RKD
integer, parameter RKD
The double precision real kind in Fortran mode. On most platforms, this is an 64-bit real kind.
Definition: pm_kind.F90:568

pm_kind::SK
integer, parameter SK
The default character kind in the ParaMonte library: kind("a") in Fortran, c_char in C-Fortran Intero...
Definition: pm_kind.F90:539

pm_kind::RKH
integer, parameter RKH
The scalar integer constant of intrinsic default kind, representing the highest-precision real kind t...
Definition: pm_kind.F90:858

pm_kind::RKS
integer, parameter RKS
The single-precision real kind in Fortran mode. On most platforms, this is an 32-bit real kind.
Definition: pm_kind.F90:567

pm_mathCompare
This module contains the procedures and interfaces for evaluating the relative or absolute proximity ...
Definition: pm_mathCompare.F90:205

pm_io::display_type
Generate and return an object of type display_type.
Definition: pm_io.F90:10282

Example Unix compile command via Intel ifort compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3ifort -fpp -standard-semantics -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example Windows Batch compile command via Intel ifort compiler ⛓
1del main.exe

2set PATH=..\..\..\lib;%PATH%

3ifort /fpp /standard-semantics /O3 /I:..\..\..\include main.F90 ..\..\..\lib\libparamonte*.lib /exe:main.exe

4main.exe

Example Unix / MinGW compile command via GNU gfortran compiler ⛓
1#!/usr/bin/env sh

2rm main.exe

3gfortran -cpp -ffree-line-length-none -O3 -Wl,-rpath,../../../lib -I../../../inc main.F90 ../../../lib/libparamonte* -o main.exe

4./main.exe

Example output ⛓
1lenData = getUnifRand(5, 100)

2lenData

3+90

4data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

5data

6(+1.90705717, +0.281345308), (+1.69471264, +0.870246887E-1), (+1.36496294, +0.410899818), (+1.20153856, +0.875982702), (+1.13179469, +0.714451969), (+1.63314462, +0.377218127), (+1.98552668, +0.371373534), (+1.98448825, +0.748443067), (+1.55443430, +0.323732674), (+1.92468727, +0.449174762), (+1.99405575, +0.512229800), (+1.47494602, +0.860334218), (+1.72274160, +0.139850914), (+1.58910644, +0.776986241), (+1.69104242, +0.178087533), (+1.61708510, +0.551339746), (+1.18150127, +0.486747026E-1), (+1.08170450, +0.647229314), (+1.43765867, +0.432701409), (+1.58834422, +0.302728653), (+1.36952901, +0.473851085), (+1.55200338, +0.611451805), (+1.79745722, +0.445368707), (+1.39768398, +0.614993870), (+1.33451128, +0.242796540), (+1.97720766, +0.458117425), (+1.42571735, +0.976924360), (+1.29636240, +0.682752311), (+1.42110920, +0.983041942), (+1.41571307, +0.979817450), (+1.21239376, +0.931666315), (+1.92617118, +0.678784609), (+1.60907841, +0.810896099), (+1.98570693, +0.805119753), (+1.61059761, +0.372045398), (+1.09965372, +0.477102458), (+1.53808367, +0.701918364), (+1.82539487, +0.127433300), (+1.10248733, +0.842454672), (+1.44130099, +0.370163023), (+1.22635484, +0.401413620), (+1.99906564, +0.120721400), (+1.02677560, +0.916647017), (+1.40086603, +0.869793952), (+1.97938466, +0.568655849), (+1.27099037, +0.821911812), (+1.59832835, +0.709797740), (+1.03783345, +0.668025017), (+1.68337417, +0.362450361), (+1.04642200, +0.416321218), (+1.36915803, +0.438977897), (+1.37303114, +0.382181048), (+1.42174351, +0.665850878), (+1.37778723, +0.102991939), (+1.35486698, +0.647794366), (+1.09164357, +0.351034999E-1), (+1.52417946, +0.776175439), (+1.88318944, +0.272536159), (+1.69600761, +0.904211819), (+1.77773595, +0.340476573), (+1.91552305, +0.999610424), (+1.46766424, +0.991741776), (+1.50921929, +0.765793920E-1), (+1.48535681, +0.168259978), (+1.39364803, +0.717925608), (+1.56912613, +0.675785542), (+1.52123463, +0.852365434), (+1.03749669, +0.742785215), (+1.89004850, +0.230014443), (+1.57577312, +0.404354811), (+1.52643561, +0.943210006), (+1.54878163, +0.810606360), (+1.34434557, +0.862632811), (+1.87986135, +0.200917721E-1), (+1.27403045, +0.929638207), (+1.92574835, +0.502029896), (+1.08841467, +0.963636994), (+1.99372172, +0.414901495), (+1.24029255, +0.838856101E-1), (+1.68250299, +0.368781686E-1), (+1.46603417, +0.190469027), (+1.26327336, +0.468194306), (+1.10211527, +0.900134981), (+1.98466182, +0.614057481), (+1.30606067, +0.337459028), (+1.42914510, +0.388973057), (+1.72418296, +0.863937318), (+1.69667459, +0.694397092), (+1.38892674, +0.156175077), (+1.35017169, +0.960684776)

7

8adat = getFFTR(getFFTF(data)) / size(data)

9adat

10(+1.90705717, +0.281345278), (+1.69471288, +0.870247707E-1), (+1.36496294, +0.410899848), (+1.20153880, +0.875982940), (+1.13179493, +0.714452088), (+1.63314426, +0.377218038), (+1.98552656, +0.371373594), (+1.98448837, +0.748443067), (+1.55443442, +0.323732764), (+1.92468739, +0.449174762), (+1.99405551, +0.512229741), (+1.47494614, +0.860334277), (+1.72274172, +0.139850870), (+1.58910656, +0.776986241), (+1.69104254, +0.178087577), (+1.61708474, +0.551339626), (+1.18150139, +0.486748070E-1), (+1.08170450, +0.647229314), (+1.43765903, +0.432701498), (+1.58834445, +0.302728623), (+1.36952877, +0.473851085), (+1.55200326, +0.611451864), (+1.79745698, +0.445368737), (+1.39768386, +0.614993870), (+1.33451116, +0.242796630), (+1.97720742, +0.458117336), (+1.42571747, +0.976924360), (+1.29636240, +0.682752311), (+1.42110920, +0.983042061), (+1.41571319, +0.979817390), (+1.21239376, +0.931666255), (+1.92617154, +0.678784668), (+1.60907853, +0.810896218), (+1.98570693, +0.805119812), (+1.61059773, +0.372045517), (+1.09965348, +0.477102190), (+1.53808379, +0.701918364), (+1.82539487, +0.127433360), (+1.10248744, +0.842454851), (+1.44130111, +0.370163053), (+1.22635484, +0.401413560), (+1.99906552, +0.120721422), (+1.02677560, +0.916647196), (+1.40086603, +0.869794011), (+1.97938502, +0.568655908), (+1.27099013, +0.821911693), (+1.59832835, +0.709797919), (+1.03783345, +0.668024898), (+1.68337440, +0.362450421), (+1.04642212, +0.416321129), (+1.36915803, +0.438977867), (+1.37303102, +0.382181168), (+1.42174339, +0.665850937), (+1.37778723, +0.102991953), (+1.35486710, +0.647794425), (+1.09164345, +0.351034179E-1), (+1.52417958, +0.776175618), (+1.88318956, +0.272536099), (+1.69600785, +0.904211998), (+1.77773571, +0.340476483), (+1.91552281, +0.999610364), (+1.46766460, +0.991741776), (+1.50921941, +0.765795782E-1), (+1.48535681, +0.168259934), (+1.39364815, +0.717925608), (+1.56912589, +0.675785303), (+1.52123475, +0.852365434), (+1.03749657, +0.742785215), (+1.89004874, +0.230014503), (+1.57577300, +0.404354900), (+1.52643538, +0.943209946), (+1.54878163, +0.810606360), (+1.34434581, +0.862632930), (+1.87986124, +0.200918522E-1), (+1.27403045, +0.929638267), (+1.92574835, +0.502029896), (+1.08841467, +0.963637114), (+1.99372137, +0.414901465), (+1.24029255, +0.838856176E-1), (+1.68250322, +0.368782245E-1), (+1.46603394, +0.190469027), (+1.26327336, +0.468194336), (+1.10211539, +0.900134981), (+1.98466182, +0.614057600), (+1.30606067, +0.337459147), (+1.42914498, +0.388972908), (+1.72418296, +0.863937438), (+1.69667459, +0.694397092), (+1.38892686, +0.156175196), (+1.35017169, +0.960684896)

11reltol = sqrt(epsilon(1._TKG))

12reltol

13+0.345266977E-3

14isClose(data, adat, reltol = reltol)

15T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

16call setAsserted(all(isClose(data, adat, reltol = reltol)))

17

18lenData = getUnifRand(5, 100)

19lenData

20+89

21data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

22data

23(+1.8866158184724633, +0.42254261131863646), (+1.9053267442970436, +0.35378442063395810), (+1.6815647515160990, +0.77263717941136334), (+1.1819643324231639, +0.25773359666914186), (+1.0347603381872008, +0.52092283705144737), (+1.7407160004142619, +0.25302552114600207), (+1.2678918315137353, +0.68862692372674683), (+1.2484492710724548, +0.53775476602220251), (+1.0696717481417473, +0.96710420454915225), (+1.1524198315487182, +0.86033928080086197), (+1.1640923556910641, +0.45137205421092452E-1), (+1.1346026244269920, +0.29204084403714947), (+1.7041070034264381, +0.38584955477314187), (+1.4219968639538418, +0.25743464433323038), (+1.4853896650895833, +0.86798969907756240), (+1.0302113176801400, +0.94118089688222284), (+1.5259072718418711, +0.80921625684922127), (+1.5042843954768701, +0.63286512552742502), (+1.0322308828250759, +0.73375339986170851), (+1.1312878209921302, +0.38455847052881931), (+1.2932711749107497, +0.34489381188832779), (+1.1624897070664315, +0.36711367605405743), (+1.7245957446120215, +0.78667461785270065E-2), (+1.9107644878193792, +0.65898822000951873E-1), (+1.6920814582243517, +0.73785761174054343), (+1.9451409719843140, +0.54941911523854048), (+1.5211592542797017, +0.33945432105706408), (+1.5563639921874182, +0.18978912588495878), (+1.5183775866199514, +0.48058588461943885), (+1.1015682627900714, +0.33999557281584569), (+1.3695629167285641, +0.72133946606624599), (+1.5491334865523454, +0.27187655207594030), (+1.7739593661063502, +0.81740968589721763), (+1.3091844929728276, +0.84717504219571738), (+1.4928183009137519, +0.25912553685936546), (+1.1053994627632295, +0.88187372794674257), (+1.6023881166196299, +0.32376323446229760), (+1.4571994201316625, +0.53071869010713058), (+1.5252917917975779, +0.40772774889921426), (+1.4610321882216040, +0.89565634473694278), (+1.5504888889313531, +0.37630210586516200), (+1.4364436084563379, +0.77451622085135796), (+1.0440741701992491, +0.52079355063671351), (+1.6996268319512664, +0.37605261866325490), (+1.9431006221362286, +0.63523204531047761E-1), (+1.5914246998865254, +0.48798996538587303), (+1.8898377025379611, +0.60351248241706168), (+1.0031650782418295, +0.79822798306180576), (+1.6721625981971939, +0.10850951535249720), (+1.0894622511497034, +0.11292188875443043), (+1.9582990060688912, +0.31974122749079070), (+1.4450215350095290, +0.57871208050578393), (+1.0970547273679938, +0.46849503907463874), (+1.8082979009648130, +0.58220709271618587), (+1.7075318737876659, +0.99680414147893404), (+1.7334664562209605, +0.91988761296537402), (+1.0740964878140455, +0.55026554897341440), (+1.7534102728848957, +0.50809562493874871), (+1.4557945195030493, +0.49038116091088646), (+1.9441726443850182, +0.77539253405083142), (+1.2002034456351076, +0.35004694779216083E-1), (+1.0290218263175939, +0.14521275615317009), (+1.2683819810058168, +0.61511781343218264), (+1.5174964594902480, +0.65918236719041168), (+1.0987110856509426, +0.30950234043606373), (+1.4901065873407640, +0.70935443503369999), (+1.8513546999014185, +0.27118389517797969), (+1.0587306189269454, +0.80172521423446708), (+1.6133571868120284, +0.10267156715264780), (+1.0420006119385943, +0.17585114559562187), (+1.0508088410793626, +0.37042668291537517), (+1.7689517814598168, +0.64866835215313934), (+1.1146492102317827, +0.53615207133982823), (+1.5294804695136013, +0.97669541963966311), (+1.8714661016601033, +0.32090615749810003), (+1.6237940251268383, +0.29697665561524833), (+1.1920958246958260, +0.37270951998405610), (+1.4129082235971824, +0.39238116434104842), (+1.1478056718060943, +0.52478845855387124), (+1.8703242958578108, +0.24034865750508949E-1), (+1.8529292732246179, +0.87598528544875698), (+1.0946248176295654, +0.69297687647242867E-1), (+1.9630521861486867, +0.63716775754185984), (+1.5202829191143765, +0.67120052413923981), (+1.6705646702076740, +0.50880502589774501), (+1.8208404833286904, +0.32084311911919305), (+1.0218253387167202, +0.54339949770920337), (+1.1368306448159415, +0.40392305820333263E-1), (+1.4995108553666743, +0.85229930159201406)

24

25adat = getFFTR(getFFTF(data)) / size(data)

26adat

27(+1.8866158184724577, +0.42254261131863469), (+1.9053267442970445, +0.35378442063395837), (+1.6815647515160996, +0.77263717941136389), (+1.1819643324231646, +0.25773359666914203), (+1.0347603381872019, +0.52092283705144771), (+1.7407160004142623, +0.25302552114600269), (+1.2678918315137364, +0.68862692372674716), (+1.2484492710724560, +0.53775476602220273), (+1.0696717481417479, +0.96710420454915269), (+1.1524198315487186, +0.86033928080086197), (+1.1640923556910641, +0.45137205421092397E-1), (+1.1346026244269924, +0.29204084403714942), (+1.7041070034264389, +0.38584955477314187), (+1.4219968639538412, +0.25743464433323049), (+1.4853896650895828, +0.86798969907756274), (+1.0302113176801400, +0.94118089688222328), (+1.5259072718418714, +0.80921625684922205), (+1.5042843954768705, +0.63286512552742535), (+1.0322308828250761, +0.73375339986170895), (+1.1312878209921304, +0.38455847052881953), (+1.2932711749107497, +0.34489381188832774), (+1.1624897070664315, +0.36711367605405748), (+1.7245957446120215, +0.78667461785270759E-2), (+1.9107644878193784, +0.65898822000951873E-1), (+1.6920814582243511, +0.73785761174054376), (+1.9451409719843142, +0.54941911523854092), (+1.5211592542797010, +0.33945432105706458), (+1.5563639921874177, +0.18978912588495883), (+1.5183775866199511, +0.48058588461943902), (+1.1015682627900716, +0.33999557281584564), (+1.3695629167285637, +0.72133946606624599), (+1.5491334865523452, +0.27187655207594025), (+1.7739593661063497, +0.81740968589721785), (+1.3091844929728282, +0.84717504219571782), (+1.4928183009137521, +0.25912553685936568), (+1.1053994627632309, +0.88187372794674246), (+1.6023881166196303, +0.32376323446229799), (+1.4571994201316631, +0.53071869010713058), (+1.5252917917975781, +0.40772774889921432), (+1.4610321882216046, +0.89565634473694256), (+1.5504888889313531, +0.37630210586516200), (+1.4364436084563383, +0.77451622085135818), (+1.0440741701992493, +0.52079355063671373), (+1.6996268319512666, +0.37605261866325529), (+1.9431006221362281, +0.63523204531047969E-1), (+1.5914246998865247, +0.48798996538587341), (+1.8898377025379609, +0.60351248241706201), (+1.0031650782418300, +0.79822798306180587), (+1.6721625981971941, +0.10850951535249743), (+1.0894622511497032, +0.11292188875443041), (+1.9582990060688914, +0.31974122749079065), (+1.4450215350095292, +0.57871208050578415), (+1.0970547273679943, +0.46849503907463891), (+1.8082979009648132, +0.58220709271618598), (+1.7075318737876668, +0.99680414147893392), (+1.7334664562209607, +0.91988761296537414), (+1.0740964878140462, +0.55026554897341484), (+1.7534102728848953, +0.50809562493874882), (+1.4557945195030491, +0.49038116091088624), (+1.9441726443850178, +0.77539253405083131), (+1.2002034456351078, +0.35004694779216292E-1), (+1.0290218263175934, +0.14521275615317025), (+1.2683819810058166, +0.61511781343218253), (+1.5174964594902476, +0.65918236719041190), (+1.0987110856509426, +0.30950234043606423), (+1.4901065873407633, +0.70935443503370021), (+1.8513546999014179, +0.27118389517797986), (+1.0587306189269454, +0.80172521423446730), (+1.6133571868120284, +0.10267156715264784), (+1.0420006119385945, +0.17585114559562184), (+1.0508088410793628, +0.37042668291537545), (+1.7689517814598170, +0.64866835215313967), (+1.1146492102317831, +0.53615207133982856), (+1.5294804695136015, +0.97669541963966378), (+1.8714661016601033, +0.32090615749810059), (+1.6237940251268381, +0.29697665561524866), (+1.1920958246958253, +0.37270951998405621), (+1.4129082235971830, +0.39238116434104853), (+1.1478056718060945, +0.52478845855387135), (+1.8703242958578103, +0.24034865750509008E-1), (+1.8529292732246179, +0.87598528544875709), (+1.0946248176295663, +0.69297687647243270E-1), (+1.9630521861486883, +0.63716775754186017), (+1.5202829191143776, +0.67120052413924014), (+1.6705646702076740, +0.50880502589774557), (+1.8208404833286915, +0.32084311911919322), (+1.0218253387167209, +0.54339949770920348), (+1.1368306448159424, +0.40392305820333901E-1), (+1.4995108553666747, +0.85229930159201428)

28reltol = sqrt(epsilon(1._TKG))

29reltol

30+0.14901161193847656E-7

31isClose(data, adat, reltol = reltol)

32T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

33call setAsserted(all(isClose(data, adat, reltol = reltol)))

34

35lenData = getUnifRand(5, 100)

36lenData

37+16

38data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

39data

40(+1.93507918301700135443440567713478989, +0.785512014694611866028141938790677165E-1), (+1.08091459706004379552931099878679070, +0.872991303293681041991315830516509128), (+1.79524436757227104851695081580793810, +0.489945373556300689477493035792544459), (+1.58973014914202092503337618616522575, +0.448702860796122933794922988341847684), (+1.38904041824298089403273859237535699, +0.157228138288092095375089267084786305E-1), (+1.66184051388195960146296963982445879, +0.701915302689470783556867184946762821), (+1.95062691251078566512806799375413599, +0.818730321630292802645763697902495424), (+1.88853414218778924278250308339862812, +0.288151663037297898931753801306939609), (+1.02059450390668472551237719705328509, +0.640265141871430243406071591404565521E-1), (+1.69066698401385722685268046251279784, +0.612193387689686122632227012711780089), (+1.81436702804850720890091057445502078, +0.709989182109312292977707644435515851), (+1.17618654459560961535169351594134388, +0.324574404613975637312129947839600676), (+1.25897804322307424484770977736734942, +0.269589662279009298287284421347376071), (+1.21343610179525198115364153829691863, +0.339450981104188485496173122240792567), (+1.90856624858456637457624277293202115, +0.909077291814069359304102470282537594), (+1.20076047437676822785631231925120724, +0.288516781035232510271866531188796858)

41

42adat = getFFTR(getFFTF(data)) / size(data)

43adat

44(+1.93507918301700135443440567713478970, +0.785512014694611866028141938790677165E-1), (+1.08091459706004379552931099878679070, +0.872991303293681041991315830516509128), (+1.79524436757227104851695081580793791, +0.489945373556300689477493035792544507), (+1.58973014914202092503337618616522595, +0.448702860796122933794922988341847684), (+1.38904041824298089403273859237535679, +0.157228138288092095375089267084786305E-1), (+1.66184051388195960146296963982445879, +0.701915302689470783556867184946762725), (+1.95062691251078566512806799375413599, +0.818730321630292802645763697902495424), (+1.88853414218778924278250308339862831, +0.288151663037297898931753801306939561), (+1.02059450390668472551237719705328490, +0.640265141871430243406071591404565521E-1), (+1.69066698401385722685268046251279784, +0.612193387689686122632227012711779993), (+1.81436702804850720890091057445502059, +0.709989182109312292977707644435515851), (+1.17618654459560961535169351594134407, +0.324574404613975637312129947839600772), (+1.25897804322307424484770977736734923, +0.269589662279009298287284421347376071), (+1.21343610179525198115364153829691863, +0.339450981104188485496173122240792471), (+1.90856624858456637457624277293202115, +0.909077291814069359304102470282537594), (+1.20076047437676822785631231925120743, +0.288516781035232510271866531188796906)

45reltol = sqrt(epsilon(1._TKG))

46reltol

47+0.138777878078144567552953958511352539E-16

48isClose(data, adat, reltol = reltol)

49T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

50call setAsserted(all(isClose(data, adat, reltol = reltol)))

51

52lenData = getUnifRand(5, 100)

53lenData

54+67

55data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

56data

57+1.94558454, +1.57588720, +1.95584440, +1.49929357, +1.22219419, +1.51891637, +1.18034911, +1.22293949, +1.34521699, +1.09916115, +1.49427187, +1.05222988, +1.93336987, +1.13276362, +1.62180901, +1.68033671, +1.84663296, +1.86109996, +1.54868460, +1.90707707, +1.52103233, +1.71052122, +1.20332050, +1.83585143, +1.43788362, +1.03243256, +1.65396285, +1.83663821, +1.67190504, +1.99092519, +1.41387725, +1.82361007, +1.99059176, +1.62947667, +1.03292775, +1.20470214, +1.06525517, +1.73895192, +1.12231493, +1.40050673, +1.98292279, +1.56661618, +1.23009121, +1.31608391, +1.68060303, +1.43710411, +1.75575638, +1.38943851, +1.91075730, +1.67248511, +1.97100568, +1.41164708, +1.11713076, +1.37536335, +1.71475601, +1.02494335, +1.56866467, +1.64404583, +1.18501544, +1.92083836, +1.78825116, +1.86027801, +1.86583459, +1.77614164, +1.27201748, +1.09877872, +1.03223753

58

59adat = getFFTR(getFFTF(data)) / size(data)

60adat

61+1.94558346, +1.57588589, +1.95584476, +1.49929333, +1.22219360, +1.51891744, +1.18034792, +1.22293878, +1.34521818, +1.09915805, +1.49427545, +1.05222237, +1.93337917, +1.13275528, +1.62181246, +1.68033576, +1.84663546, +1.86110294, +1.54868019, +1.90708447, +1.52102840, +1.71052790, +1.20330977, +1.83586264, +1.43788302, +1.03242123, +1.65396726, +1.83664405, +1.67190158, +1.99093783, +1.41386497, +1.82361388, +1.99060059, +1.62948489, +1.03291845, +1.20470273, +1.06524408, +1.73896849, +1.12230396, +1.40050459, +1.98293662, +1.56661594, +1.23008633, +1.31607962, +1.68060994, +1.43709910, +1.75576341, +1.38943112, +1.91076529, +1.67248225, +1.97101355, +1.41164482, +1.11712635, +1.37536252, +1.71476197, +1.02493668, +1.56866658, +1.64404869, +1.18501043, +1.92084146, +1.78825092, +1.86027825, +1.86583495, +1.77614212, +1.27201664, +1.09877777, +1.03223622

62reltol = sqrt(epsilon(1._TKG))

63reltol

64+0.345266977E-3

65isClose(data, adat, reltol = reltol)

66T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

67call setAsserted(all(isClose(data, adat, reltol = reltol)))

68

69lenData = getUnifRand(5, 100)

70lenData

71+44

72data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

73data

74+1.8220313555016281, +1.2432380445426405, +1.4721619769704892, +1.9113205259603654, +1.2866886412674927, +1.4913854196247587, +1.4745989216178996, +1.9072131355753736, +1.6244243499906081, +1.2748481119761739, +1.8604245346048949, +1.2140843557031151, +1.8462586216616641, +1.4221772039958767, +1.8430679701754800, +1.3638955117867704, +1.5260614527866436, +1.6066287128923782, +1.0137857778543733, +1.8412585248110191, +1.8294615849672693, +1.5861230337184853, +1.6295530208429079, +1.1575891475917017, +1.0970895820988931, +1.3709036363232667, +1.2722156020494362, +1.5858314694156368, +1.0540025061549334, +1.4600313787553119, +1.0048774673851546, +1.8729005166333266, +1.6023062402364028, +1.5775725781072687, +1.8747738288445210, +1.6644859292088792, +1.5861591868607583, +1.3993971354024879, +1.4052478684073941, +1.3145009624691435, +1.2205414590456640, +1.2528928058076256, +1.9611040725084767, +1.3437210202629237

75

76adat = getFFTR(getFFTF(data)) / size(data)

77adat

78+1.8220313555016283, +1.2432380445426412, +1.4721619769704894, +1.9113205259603661, +1.2866886412674921, +1.4913854196247589, +1.4745989216178996, +1.9072131355753739, +1.6244243499906077, +1.2748481119761741, +1.8604245346048953, +1.2140843557031160, +1.8462586216616637, +1.4221772039958769, +1.8430679701754793, +1.3638955117867708, +1.5260614527866436, +1.6066287128923782, +1.0137857778543737, +1.8412585248110198, +1.8294615849672682, +1.5861230337184851, +1.6295530208429063, +1.1575891475917017, +1.0970895820988920, +1.3709036363232665, +1.2722156020494351, +1.5858314694156368, +1.0540025061549334, +1.4600313787553121, +1.0048774673851550, +1.8729005166333272, +1.6023062402364021, +1.5775725781072687, +1.8747738288445204, +1.6644859292088798, +1.5861591868607583, +1.3993971354024881, +1.4052478684073944, +1.3145009624691442, +1.2205414590456636, +1.2528928058076259, +1.9611040725084763, +1.3437210202629239

79reltol = sqrt(epsilon(1._TKG))

80reltol

81+0.14901161193847656E-7

82isClose(data, adat, reltol = reltol)

83T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

84call setAsserted(all(isClose(data, adat, reltol = reltol)))

85

86lenData = getUnifRand(5, 100)

87lenData

88+66

89data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

90data

91+1.97788832111786188875835883453177358, +1.72960512098492019085384403464023534, +1.36387213382067424487930980882311494, +1.91389995278447778437478693832247346, +1.35027093040909890366409424884577127, +1.83847353518729197903285327322833762, +1.78604979733287904768580022401173039, +1.16211878388239692113676767728855861, +1.02441008364115233756129020882542672, +1.80591349556690162285230119001044869, +1.66251096018246431579212041084487812, +1.75129941426452371879447065303869076, +1.57411549967667418480468802394954248, +1.16823448269868831453147281332985730, +1.31522484300616625063964653154060382, +1.58124538182180568723352732458007848, +1.32810860013300805795183752901572353, +1.52094367911889340142407354984076806, +1.35168648224964903145078614290843680, +1.38694304209692306070026216273223472, +1.37019250917320815532916375791926459, +1.26055808332693117164130261301040472, +1.03473362267639267408854192426414227, +1.64112816894273090103902265058178969, +1.04111892322643109108592239636834927, +1.34713561595120443931520000734647146, +1.55701244323360210926343441093717634, +1.15124291443201478618806237150525274, +1.15102838067830171028427959050208916, +1.16957396862568748155541404797338520, +1.38255218090150473328251066264197558, +1.54531285099437551704320609199701754, +1.44976189627953018048708699136163067, +1.66979850789912146914732832323626204, +1.06180503364837046748151280540863951, +1.18376854537674999012807874717321945, +1.14525722863574165710534196732897306, +1.06380385114534131386379883418535080, +1.41532327882788197712154385455929273, +1.94954362456930495673716423345777769, +1.23692945758623411037056013399360236, +1.53643458643241913247949999911742558, +1.00225594484231208778806552897583491, +1.15643907799904412922488469509503153, +1.65850788544383582547384229499352010, +1.81814294491229678734617772627691883, +1.58384117312361599098530475109948639, +1.67133046084882539630170532906872497, +1.66787205311783813221332707273886377, +1.81880848869076072624992667625675830, +1.81542351753169528698727278919418568, +1.02102963508408935762118329450125158, +1.13740931798985381015539185270541269, +1.39200081791009337493044674777080642, +1.20997891146193507804516406585210828, +1.15728132183260415617030457334169883, +1.19983397318937195392452653397802920, +1.57112778914203144321381129028557075, +1.58572434571155759353033934468091860, +1.97979542867143561619407010771021542, +1.12965777037938964935866371296965642, +1.67517718139153094024986075917467144, +1.29381471812137715970460197153674871, +1.51209777187992872636006078786504878, +1.54138069921100872044849256364663012, +1.75326039585498907803621065765912155

92

93adat = getFFTR(getFFTF(data)) / size(data)

94adat

95+1.97788832111786188875835883453177454, +1.72960512098492019085384403464023572, +1.36387213382067424487930980882311532, +1.91389995278447778437478693832247384, +1.35027093040909890366409424884577127, +1.83847353518729197903285327322833782, +1.78604979733287904768580022401173039, +1.16211878388239692113676767728855842, +1.02441008364115233756129020882542672, +1.80591349556690162285230119001044831, +1.66251096018246431579212041084487812, +1.75129941426452371879447065303869018, +1.57411549967667418480468802394954268, +1.16823448269868831453147281332985749, +1.31522484300616625063964653154060440, +1.58124538182180568723352732458007867, +1.32810860013300805795183752901572411, +1.52094367911889340142407354984076787, +1.35168648224964903145078614290843661, +1.38694304209692306070026216273223433, +1.37019250917320815532916375791926440, +1.26055808332693117164130261301040434, +1.03473362267639267408854192426414227, +1.64112816894273090103902265058178892, +1.04111892322643109108592239636834985, +1.34713561595120443931520000734647184, +1.55701244323360210926343441093717711, +1.15124291443201478618806237150525293, +1.15102838067830171028427959050208936, +1.16957396862568748155541404797338520, +1.38255218090150473328251066264197500, +1.54531285099437551704320609199701696, +1.44976189627953018048708699136163009, +1.66979850789912146914732832323626069, +1.06180503364837046748151280540863912, +1.18376854537674999012807874717321829, +1.14525722863574165710534196732897228, +1.06380385114534131386379883418535003, +1.41532327882788197712154385455929215, +1.94954362456930495673716423345777654, +1.23692945758623411037056013399360197, +1.53643458643241913247949999911742461, +1.00225594484231208778806552897583568, +1.15643907799904412922488469509503173, +1.65850788544383582547384229499352068, +1.81814294491229678734617772627691922, +1.58384117312361599098530475109948658, +1.67133046084882539630170532906872497, +1.66787205311783813221332707273886357, +1.81880848869076072624992667625675811, +1.81542351753169528698727278919418568, +1.02102963508408935762118329450125100, +1.13740931798985381015539185270541250, +1.39200081791009337493044674777080565, +1.20997891146193507804516406585210828, +1.15728132183260415617030457334169921, +1.19983397318937195392452653397802959, +1.57112778914203144321381129028557094, +1.58572434571155759353033934468091918, +1.97979542867143561619407010771021523, +1.12965777037938964935866371296965642, +1.67517718139153094024986075917467105, +1.29381471812137715970460197153674832, +1.51209777187992872636006078786504840, +1.54138069921100872044849256364663012, +1.75326039585498907803621065765912097

96reltol = sqrt(epsilon(1._TKG))

97reltol

98+0.138777878078144567552953958511352539E-16

99isClose(data, adat, reltol = reltol)

100T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

101call setAsserted(all(isClose(data, adat, reltol = reltol)))

102

103lenData = getUnifRand(5, 100)

104lenData

105+5

106data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

107data

108(+1.11534274, +0.891265869), (+1.37895739, +0.571308076), (+1.56183696, +0.666329443), (+1.58125615, +0.771801889), (+1.31753755, +0.458028138)

109

110adat = getFFTR(getFFTF(data)) / size(data)

111adat

112(+1.11534250, +0.891265750), (+1.37895751, +0.571308017), (+1.56183696, +0.666329443), (+1.58125615, +0.771801889), (+1.31753755, +0.458028138)

113reltol = sqrt(epsilon(1._TKG))

114reltol

115+0.345266977E-3

116isClose(data, adat, reltol = reltol)

117T, T, T, T, T

118call setAsserted(all(isClose(data, adat, reltol = reltol)))

119

120lenData = getUnifRand(5, 100)

121lenData

122+49

123data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

124data

125(+1.1005282096874387, +0.61628276054104303), (+1.9610988306865700, +0.48902014816982520), (+1.6635561675973003, +0.45790937242724783), (+1.2642532186791862, +0.77330960527482651), (+1.5025267340044517, +0.28461566248132120E-1), (+1.0481084801865324, +0.75205003403966242), (+1.8265907468277454, +0.59447651725758521), (+1.6332307771937646, +0.26794997973412382), (+1.1666710689617963, +0.75086914191210408), (+1.0231975976722962, +0.48458524395918190), (+1.6027653528135872, +0.68970458184925421E-1), (+1.9065193748527383, +0.25618041505171985), (+1.9846406206370397, +0.32357716245826396E-1), (+1.1599399538027872, +0.89166269292958755), (+1.3082907315403471, +0.97100585564759201E-1), (+1.6278043390749399, +0.28080807572381250), (+1.7087156823891989, +0.51855158258353407E-1), (+1.2278598110555428, +0.15430889256527081), (+1.5926923463950597, +0.27517978330924520), (+1.6060708147791929, +0.88738498104698127), (+1.2802387933786741, +0.57267922961313555), (+1.7938243537888452, +0.69109581456699887), (+1.3422344313150754, +0.65739744242419718), (+1.7252209575324180, +0.15606203200069468), (+1.4760288461016375, +0.39439975297430430), (+1.1487261001204097, +0.82265889145926252), (+1.7323123331087140, +0.72505799714278862), (+1.7997477563703730, +0.35222333297025343), (+1.7453450952336400, +0.32220023581890678), (+1.9674695708977064, +0.22373690513367972), (+1.0902761767869475, +0.32655835853891868), (+1.8012655668812911, +0.48184457268393477), (+1.7421865933678999, +0.54445362468728598), (+1.6932941852973666, +0.46316677775083614), (+1.4659569146815592, +0.22790955021833637), (+1.7392537510171922, +0.27627822671040236), (+1.7483559132707571, +0.71405437104610803), (+1.1101323154949911, +0.27551837717742989), (+1.4156221880562538, +0.52971365682623062E-1), (+1.4102910295186581, +0.48436388645651318), (+1.6471430813809411, +0.71902031930211152), (+1.8077819307722760, +0.20050523327830738), (+1.6528710729021094, +0.24770430897268414), (+1.0666325808737920, +0.39755975664547449), (+1.9003061529105549, +0.43861814592538662), (+1.4165923480799751, +0.57188933543840148), (+1.3523508410866187, +0.78020994879421823), (+1.0498413855517374, +0.63789930761294178), (+1.7286240493995173, +0.41476468233760111)

126

127adat = getFFTR(getFFTF(data)) / size(data)

128adat

129(+1.1005282096874387, +0.61628276054104303), (+1.9610988306865702, +0.48902014816982536), (+1.6635561675973001, +0.45790937242724794), (+1.2642532186791862, +0.77330960527482662), (+1.5025267340044519, +0.28461566248131953E-1), (+1.0481084801865321, +0.75205003403966231), (+1.8265907468277458, +0.59447651725758532), (+1.6332307771937649, +0.26794997973412393), (+1.1666710689617965, +0.75086914191210408), (+1.0231975976722962, +0.48458524395918190), (+1.6027653528135870, +0.68970458184925518E-1), (+1.9065193748527385, +0.25618041505171979), (+1.9846406206370397, +0.32357716245826541E-1), (+1.1599399538027877, +0.89166269292958777), (+1.3082907315403467, +0.97100585564759298E-1), (+1.6278043390749402, +0.28080807572381256), (+1.7087156823891989, +0.51855158258353413E-1), (+1.2278598110555428, +0.15430889256527075), (+1.5926923463950602, +0.27517978330924514), (+1.6060708147791929, +0.88738498104698105), (+1.2802387933786743, +0.57267922961313555), (+1.7938243537888443, +0.69109581456699898), (+1.3422344313150756, +0.65739744242419718), (+1.7252209575324180, +0.15606203200069466), (+1.4760288461016366, +0.39439975297430396), (+1.1487261001204097, +0.82265889145926208), (+1.7323123331087138, +0.72505799714278829), (+1.7997477563703732, +0.35222333297025354), (+1.7453450952336396, +0.32220023581890667), (+1.9674695708977066, +0.22373690513367978), (+1.0902761767869473, +0.32655835853891868), (+1.8012655668812905, +0.48184457268393477), (+1.7421865933678999, +0.54445362468728553), (+1.6932941852973666, +0.46316677775083592), (+1.4659569146815592, +0.22790955021833617), (+1.7392537510171922, +0.27627822671040253), (+1.7483559132707571, +0.71405437104610836), (+1.1101323154949911, +0.27551837717742989), (+1.4156221880562538, +0.52971365682622985E-1), (+1.4102910295186586, +0.48436388645651318), (+1.6471430813809409, +0.71902031930211152), (+1.8077819307722762, +0.20050523327830733), (+1.6528710729021092, +0.24770430897268425), (+1.0666325808737926, +0.39755975664547466), (+1.9003061529105547, +0.43861814592538645), (+1.4165923480799751, +0.57188933543840137), (+1.3523508410866187, +0.78020994879421812), (+1.0498413855517374, +0.63789930761294200), (+1.7286240493995177, +0.41476468233760139)

130reltol = sqrt(epsilon(1._TKG))

131reltol

132+0.14901161193847656E-7

133isClose(data, adat, reltol = reltol)

134T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

135call setAsserted(all(isClose(data, adat, reltol = reltol)))

136

137lenData = getUnifRand(5, 100)

138lenData

139+61

140data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

141data

142(+1.40010417017162522271297164246653900, +0.944885551070933109183491666206704022), (+1.23350640488132629475794349496022250, +0.999967575024394221280860308683894066E-1), (+1.12344170085938869571872522931136260, +0.254669918965893836901377712781084752), (+1.29927660488597972070074478787080781, +0.569662229678729986939240756081452248), (+1.96305489260263415452980556146258046, +0.692571089117786643870037339615840759), (+1.73253233931483659629296392578728824, +0.426259092692244773214499333002087645), (+1.86368686763483458565601515957950009, +0.848605151247643186471479431882892430), (+1.39382402038251758010661928204485087, +0.234121649099116475404211840652130498), (+1.14945355776546945700395792938553381, +0.281741942037527395065425372771911784), (+1.65596726462834618377005591748209958, +0.820663054148674126369765705300853863), (+1.79761392853898724232735894526565351, +0.749846448785225044412147890306465927), (+1.85778972176894623970698239782714090, +0.885081802355728383666668375153229227), (+1.94023754540420551821208132722375836, +0.350282980980571761929292288973510069), (+1.96115175702599950370853341934574834, +0.467891497378234612184242098917059697), (+1.52516874559130655758759602015781279, +0.717436181296068260657676440567432341), (+1.11507995322899988494097544556784746, +0.710958258663933578644829554431573022), (+1.02735690266865891243809828247275056, +0.969430185860436147991090581741916030), (+1.45728592833563262214914286141946503, +0.537170825140019770997017215134669990), (+1.03724442779645550741072494443891463, +0.368775247666924294569659313893333296), (+1.71119224945686460234277619997982601, +0.459283434443785162901619245219708362), (+1.71374795835073327030360716597558278, +0.596304916382398662024051958372527019), (+1.53757652578067728411261868092516109, +0.598337842499003998361168726760744112), (+1.70308958139588364528861610376260789, +0.561043697263715537746751116519469374), (+1.88330346389898738238007162792064265, +0.624367916236024851852927860528847988), (+1.87903635982919326264013927722614330, +0.300697763380061978386037911569373368), (+1.49844803198622912471872832876909285, +0.824365663473977383614201895112252432), (+1.56409473100644932491667792514194361, +0.386863982735312762504302185326118484), (+1.10241276495013222887614121886975489, +0.487335843835587201506272020705979837), (+1.34030830051597119026955629628632580, +0.764941647549648890461762786904497787E-1), (+1.75905691018548551451410194481094153, +0.667269427614871558039580361785114056), (+1.55678346642432609292650802687123259, +0.277797121103122565457828341914111423), (+1.96515983488381156361246922823270672, +0.831135490378744442101673651094120610), (+1.76949770485128971404774912947951983, +0.861585348162051093043547790764946387), (+1.96240425566362482612612320654947486, +0.431066761074064360473879648346291775), (+1.41951995225208738058389286619641423, +0.234484065077926901305018781928941162), (+1.65924468249382542088061101898421484, +0.215635331648022790124947173291820114), (+1.05830410170053863405458705052669107, +0.381276677963833597040556762637686098), (+1.38338699818737983385449367293771177, +0.430411067237434764262415858256072555), (+1.71012674884411645731308846579579172, +0.623086990389904540708980469501070839), (+1.24095829951657507876403975432617723, +0.426184695084078444859137806589231040), (+1.07126193044460228753564506504333456, +0.254955714251811197741150853952993259), (+1.03536210199623054850324202767129560, +0.922384077614393553559374512170640007), (+1.31710543579434761379731824263334424, +0.457150597958647607911352195917098892), (+1.06891401270233694598296439938983747, +0.773215543719565498053963381557162500), (+1.54715407528649237171702559046327406, +0.831666246288853595310722167718242473), (+1.11580657906524111587053210560479224, +0.636512410062735198168551476901553565E-1), (+1.38845503347226602976501763207733019, +0.448182409315564487905917766017384708), (+1.11766201605714493845356118300010313, +0.844810837644332314231659997536332283), (+1.82953417816835718214925800558418145, +0.445267172904235066602834166559880789E-1), (+1.06369821561830412566529268947899378, +0.288201057830499059389744756825831477), (+1.17225553598539017855678838727599148, +0.245028980170905732005147281837255117), (+1.05072253947893798437841018811527606, +0.115957342773434728407007928123122478), (+1.98940462953785535737627238479865488, +0.933468409323984812919115043838177726), (+1.65747725039137280256186196057463936, +0.321307946569374484164228848827547337), (+1.00540827830064634618284121029164827, +0.362599795120817638617738389656785037), (+1.47631235731241725472405204697847292, +0.286605602045214809967803477239610057E-1), (+1.16683329990625660650030234978660794, +0.453063431546580571668180547222569407), (+1.75485721497082560356985479903973594, +0.912744220436047666514354366809935563), (+1.68454386611207092824416723175642538, +0.116924884554974332155243453312419533), (+1.28452839806373769140393103008172467, +0.941450057066616515198571150011338832), (+1.52683988321818158007413119610613507, +0.287616813097160894222563443460719346)

143

144adat = getFFTR(getFFTF(data)) / size(data)

145adat

146(+1.40010417017162522271297164246654016, +0.944885551070933109183491666206704311), (+1.23350640488132629475794349496022231, +0.999967575024394221280860308683893826E-1), (+1.12344170085938869571872522931136338, +0.254669918965893836901377712781084800), (+1.29927660488597972070074478787080800, +0.569662229678729986939240756081452152), (+1.96305489260263415452980556146258085, +0.692571089117786643870037339615840663), (+1.73253233931483659629296392578728843, +0.426259092692244773214499333002087452), (+1.86368686763483458565601515957949951, +0.848605151247643186471479431882892044), (+1.39382402038251758010661928204485125, +0.234121649099116475404211840652130353), (+1.14945355776546945700395792938553400, +0.281741942037527395065425372771911736), (+1.65596726462834618377005591748209958, +0.820663054148674126369765705300853959), (+1.79761392853898724232735894526565294, +0.749846448785225044412147890306465542), (+1.85778972176894623970698239782714052, +0.885081802355728383666668375153229035), (+1.94023754540420551821208132722375855, +0.350282980980571761929292288973510021), (+1.96115175702599950370853341934574872, +0.467891497378234612184242098917059793), (+1.52516874559130655758759602015781298, +0.717436181296068260657676440567432245), (+1.11507995322899988494097544556784746, +0.710958258663933578644829554431572926), (+1.02735690266865891243809828247275094, +0.969430185860436147991090581741915838), (+1.45728592833563262214914286141946445, +0.537170825140019770997017215134670087), (+1.03724442779645550741072494443891444, +0.368775247666924294569659313893333344), (+1.71119224945686460234277619997982582, +0.459283434443785162901619245219708122), (+1.71374795835073327030360716597558278, +0.596304916382398662024051958372526923), (+1.53757652578067728411261868092516051, +0.598337842499003998361168726760743727), (+1.70308958139588364528861610376260789, +0.561043697263715537746751116519469470), (+1.88330346389898738238007162792064130, +0.624367916236024851852927860528848084), (+1.87903635982919326264013927722614311, +0.300697763380061978386037911569373561), (+1.49844803198622912471872832876909266, +0.824365663473977383614201895112252336), (+1.56409473100644932491667792514194361, +0.386863982735312762504302185326118532), (+1.10241276495013222887614121886975470, +0.487335843835587201506272020705980029), (+1.34030830051597119026955629628632541, +0.764941647549648890461762786904497185E-1), (+1.75905691018548551451410194481094134, +0.667269427614871558039580361785113960), (+1.55678346642432609292650802687123163, +0.277797121103122565457828341914111182), (+1.96515983488381156361246922823270556, +0.831135490378744442101673651094120610), (+1.76949770485128971404774912947951964, +0.861585348162051093043547790764946387), (+1.96240425566362482612612320654947467, +0.431066761074064360473879648346291727), (+1.41951995225208738058389286619641404, +0.234484065077926901305018781928941307), (+1.65924468249382542088061101898421484, +0.215635331648022790124947173291820234), (+1.05830410170053863405458705052669088, +0.381276677963833597040556762637686049), (+1.38338699818737983385449367293771158, +0.430411067237434764262415858256072796), (+1.71012674884411645731308846579579056, +0.623086990389904540708980469501070935), (+1.24095829951657507876403975432617742, +0.426184695084078444859137806589230944), (+1.07126193044460228753564506504333398, +0.254955714251811197741150853952992825), (+1.03536210199623054850324202767129560, +0.922384077614393553559374512170640200), (+1.31710543579434761379731824263334405, +0.457150597958647607911352195917098458), (+1.06891401270233694598296439938983708, +0.773215543719565498053963381557162597), (+1.54715407528649237171702559046327367, +0.831666246288853595310722167718242376), (+1.11580657906524111587053210560479262, +0.636512410062735198168551476901552000E-1), (+1.38845503347226602976501763207733019, +0.448182409315564487905917766017384564), (+1.11766201605714493845356118300010294, +0.844810837644332314231659997536332091), (+1.82953417816835718214925800558418184, +0.445267172904235066602834166559881571E-1), (+1.06369821561830412566529268947899397, +0.288201057830499059389744756825831477), (+1.17225553598539017855678838727599110, +0.245028980170905732005147281837255166), (+1.05072253947893798437841018811527606, +0.115957342773434728407007928123122454), (+1.98940462953785535737627238479865507, +0.933468409323984812919115043838177630), (+1.65747725039137280256186196057463975, +0.321307946569374484164228848827547192), (+1.00540827830064634618284121029164866, +0.362599795120817638617738389656784989), (+1.47631235731241725472405204697847254, +0.286605602045214809967803477239608372E-1), (+1.16683329990625660650030234978660833, +0.453063431546580571668180547222569455), (+1.75485721497082560356985479903973613, +0.912744220436047666514354366809935371), (+1.68454386611207092824416723175642538, +0.116924884554974332155243453312419569), (+1.28452839806373769140393103008172544, +0.941450057066616515198571150011338832), (+1.52683988321818158007413119610613488, +0.287616813097160894222563443460719249)

147reltol = sqrt(epsilon(1._TKG))

148reltol

149+0.138777878078144567552953958511352539E-16

150isClose(data, adat, reltol = reltol)

151T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

152call setAsserted(all(isClose(data, adat, reltol = reltol)))

153

154lenData = getUnifRand(5, 100)

155lenData

156+25

157data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

158data

159+1.61207390, +1.23650157, +1.78560698, +1.04221678, +1.54343820, +1.61037540, +1.01422429, +1.74123681, +1.53334379, +1.53306770, +1.07629812, +1.48277092, +1.83198404, +1.29959345, +1.24543834, +1.36483455, +1.42859817, +1.50116765, +1.10729575, +1.25158834, +1.88921547, +1.43255520, +1.40934575, +1.97496009, +1.84677124

160

161adat = getFFTR(getFFTF(data)) / size(data)

162adat

163+1.61207318, +1.23650134, +1.78560698, +1.04221654, +1.54343796, +1.61037517, +1.01422429, +1.74123716, +1.53334379, +1.53306758, +1.07629776, +1.48277104, +1.83198428, +1.29959345, +1.24543834, +1.36483419, +1.42859828, +1.50116789, +1.10729587, +1.25158823, +1.88921523, +1.43255520, +1.40934598, +1.97495997, +1.84677124

164reltol = sqrt(epsilon(1._TKG))

165reltol

166+0.345266977E-3

167isClose(data, adat, reltol = reltol)

168T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

169call setAsserted(all(isClose(data, adat, reltol = reltol)))

170

171lenData = getUnifRand(5, 100)

172lenData

173+15

174data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

175data

176+1.0140195470762099, +1.1632037373386708, +1.3733412826512621, +1.0117941429025319, +1.5498466622664333, +1.2534009895869467, +1.4389362669257000, +1.1498317907044999, +1.3258772863644710, +1.9372591656857230, +1.5730986644014324, +1.7677126216148582, +1.2482952924758355, +1.4340161642296096, +1.7213392330684232

177

178adat = getFFTR(getFFTF(data)) / size(data)

179adat

180+1.0140195470762101, +1.1632037373386708, +1.3733412826512621, +1.0117941429025319, +1.5498466622664331, +1.2534009895869465, +1.4389362669257002, +1.1498317907044997, +1.3258772863644708, +1.9372591656857234, +1.5730986644014322, +1.7677126216148580, +1.2482952924758355, +1.4340161642296094, +1.7213392330684230

181reltol = sqrt(epsilon(1._TKG))

182reltol

183+0.14901161193847656E-7

184isClose(data, adat, reltol = reltol)

185T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

186call setAsserted(all(isClose(data, adat, reltol = reltol)))

187

188lenData = getUnifRand(5, 100)

189lenData

190+48

191data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

192data

193+1.36224092264489534818813205935129441, +1.56843213978996140537676643856571549, +1.47428486529054664118557084733971259, +1.33124004785970529009016318960768528, +1.99799392628597637581107594885079414, +1.22108325042265081311021934463771921, +1.64202510955385009599300664049508810, +1.01845402570326594020054390285962968, +1.72799099033335420360980864632868805, +1.94512793518016184835656393137092635, +1.65054082183657048652159035585875756, +1.50171096001675260653178503310241560, +1.50177475146244480822085864814577678, +1.75974858304776184677807463372351581, +1.52247375848538459253958684198331111, +1.56851182687531511791000665761802413, +1.60856407575936725319360959610675165, +1.36506886257264909630492753904195475, +1.73327417353373939488173728260034698, +1.88523878787817566026823029045787874, +1.28758919087101803353502394524095873, +1.63895156617216744841318030081071422, +1.66012168904841767945614792647425338, +1.82310995888548144241727974096504358, +1.26860938304042411322776697967837286, +1.82549673215546642992022112257289511, +1.98048703697941288305494416672998009, +1.44757996786966279475556681478099855, +1.01292024806814806093549807380948836, +1.46462753488015212982221602129611159, +1.04099731699655335615317355724957989, +1.50753679641855657430727218674157371, +1.63714256815796265453886491254919528, +1.98929263129835544598054659397951967, +1.69151012988830200070710690288319907, +1.79187644593473651081021503717069152, +1.00916316261397030416275699381190005, +1.60161290458738085249949328425240199, +1.69475168858203571745715403478735188, +1.20972141591700808213562370938456104, +1.25834236593105128709730864978426199, +1.27490816643358031122785148242708292, +1.03137583877994273490581152066424528, +1.33590524171094246376073986426385166, +1.24827614644240808132780436041505831, +1.20944727531884568377939415219229499, +1.26690091832882133237381068298197423, +1.07259135685180713432570853067522342

194

195adat = getFFTR(getFFTF(data)) / size(data)

196adat

197+1.36224092264489534818813205935129461, +1.56843213978996140537676643856571607, +1.47428486529054664118557084733971239, +1.33124004785970529009016318960768528, +1.99799392628597637581107594885079356, +1.22108325042265081311021934463771959, +1.64202510955385009599300664049508790, +1.01845402570326594020054390285962987, +1.72799099033335420360980864632868824, +1.94512793518016184835656393137092654, +1.65054082183657048652159035585875717, +1.50171096001675260653178503310241579, +1.50177475146244480822085864814577659, +1.75974858304776184677807463372351581, +1.52247375848538459253958684198331092, +1.56851182687531511791000665761802432, +1.60856407575936725319360959610675146, +1.36506886257264909630492753904195533, +1.73327417353373939488173728260034640, +1.88523878787817566026823029045787893, +1.28758919087101803353502394524095854, +1.63895156617216744841318030081071461, +1.66012168904841767945614792647425338, +1.82310995888548144241727974096504396, +1.26860938304042411322776697967837305, +1.82549673215546642992022112257289511, +1.98048703697941288305494416672997951, +1.44757996786966279475556681478099874, +1.01292024806814806093549807380948817, +1.46462753488015212982221602129611159, +1.04099731699655335615317355724957989, +1.50753679641855657430727218674157429, +1.63714256815796265453886491254919528, +1.98929263129835544598054659397952044, +1.69151012988830200070710690288319869, +1.79187644593473651081021503717069152, +1.00916316261397030416275699381189986, +1.60161290458738085249949328425240218, +1.69475168858203571745715403478735150, +1.20972141591700808213562370938456142, +1.25834236593105128709730864978426218, +1.27490816643358031122785148242708311, +1.03137583877994273490581152066424490, +1.33590524171094246376073986426385186, +1.24827614644240808132780436041505811, +1.20944727531884568377939415219229499, +1.26690091832882133237381068298197404, +1.07259135685180713432570853067522380

198reltol = sqrt(epsilon(1._TKG))

199reltol

200+0.138777878078144567552953958511352539E-16

201isClose(data, adat, reltol = reltol)

202T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

203call setAsserted(all(isClose(data, adat, reltol = reltol)))

204

205lenData = getUnifRand(5, 100)

206lenData

207+47

208data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

209data

210(+1.31203127, +0.343071759), (+1.72243810, +0.749704838E-1), (+1.21891451, +0.465488672), (+1.09421945, +0.866405368), (+1.43797934, +0.655910254), (+1.42775154, +0.287748516), (+1.36935616, +0.126824856), (+1.75592148, +0.380837083), (+1.35131502, +0.901698887), (+1.60218918, +0.304731131), (+1.63834918, +0.288382709), (+1.00605559, +0.532346368), (+1.68085039, +0.784960389), (+1.95559263, +0.983515859), (+1.10316944, +0.876017392), (+1.17472625, +0.474172235E-1), (+1.08515000, +0.570378721), (+1.66463566, +0.932237208), (+1.69503736, +0.402041674), (+1.98372793, +0.849182010), (+1.18250394, +0.761804819), (+1.32619190, +0.109247565), (+1.25180221, +0.453422427), (+1.19336987, +0.486279011), (+1.79080164, +0.990539670), (+1.84873199, +0.389062941), (+1.16910815, +0.634323478), (+1.98758912, +0.697141290), (+1.53609872, +0.122433603), (+1.65084863, +0.157177687), (+1.25529099, +0.104409397), (+1.25932264, +0.165902793), (+1.41543925, +0.757900476E-1), (+1.71544993, +0.815715313), (+1.19810414, +0.856083572), (+1.57269049, +0.371772170), (+1.21583295, +0.302851796E-1), (+1.39871216, +0.486293256), (+1.20312643, +0.328318119), (+1.49964619, +0.510944843), (+1.46068847, +0.923168898), (+1.61835766, +0.779953718), (+1.24702549, +0.667694509), (+1.67621875, +0.377906203), (+1.79884219, +0.843798578), (+1.45523095, +0.137647510), (+1.56570232, +0.333205700)

211

212adat = getFFTR(getFFTF(data)) / size(data)

213adat

214(+1.31203270, +0.343072146), (+1.72243738, +0.749701634E-1), (+1.21891391, +0.465488583), (+1.09421909, +0.866405189), (+1.43797934, +0.655910194), (+1.42775130, +0.287748367), (+1.36935604, +0.126824886), (+1.75592136, +0.380837023), (+1.35131419, +0.901699007), (+1.60218871, +0.304731071), (+1.63834882, +0.288382620), (+1.00605559, +0.532346308), (+1.68085027, +0.784960508), (+1.95559227, +0.983515620), (+1.10316885, +0.876017213), (+1.17472577, +0.474171750E-1), (+1.08515000, +0.570378721), (+1.66463590, +0.932237208), (+1.69503748, +0.402041614), (+1.98372746, +0.849182069), (+1.18250418, +0.761804879), (+1.32619178, +0.109247431), (+1.25180292, +0.453422457), (+1.19337046, +0.486279339), (+1.79080212, +0.990539968), (+1.84873259, +0.389063001), (+1.16910815, +0.634323359), (+1.98758936, +0.697141528), (+1.53609824, +0.122433849), (+1.65084875, +0.157177687), (+1.25529110, +0.104409404), (+1.25932264, +0.165902823), (+1.41543877, +0.757898241E-1), (+1.71544921, +0.815715134), (+1.19810367, +0.856083333), (+1.57269049, +0.371772289), (+1.21583295, +0.302851256E-1), (+1.39871180, +0.486293197), (+1.20312595, +0.328318030), (+1.49964535, +0.510944963), (+1.46068847, +0.923168898), (+1.61835742, +0.779953718), (+1.24702525, +0.667694390), (+1.67621875, +0.377906233), (+1.79884207, +0.843798280), (+1.45523024, +0.137647420), (+1.56570172, +0.333205402)

215reltol = sqrt(epsilon(1._TKG))

216reltol

217+0.345266977E-3

218isClose(data, adat, reltol = reltol)

219T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

220call setAsserted(all(isClose(data, adat, reltol = reltol)))

221

222lenData = getUnifRand(5, 100)

223lenData

224+44

225data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

226data

227(+1.5595301572292177, +0.78084858314063732), (+1.8415966353195046, +0.33126764059824509E-1), (+1.5474046818316609, +0.70693853994845024), (+1.9916360715032253, +0.84426092444811474E-2), (+1.6942413142225994, +0.23577952398009228), (+1.5283428010624287, +0.52500238029302926E-1), (+1.4565027838252864, +0.58156552943960960), (+1.2571878577159046, +0.13577479625130395), (+1.8042915957534418, +0.70627949771688869), (+1.8280852055082601, +0.63851413042427607), (+1.6827508591670171, +0.32265290612709940), (+1.6680861607467767, +0.73637385418913293E-1), (+1.0678443579329737, +0.27634137325274555), (+1.2553500261876174, +0.13413664545991988), (+1.2759095049342764, +0.18678948229212045), (+1.8546541235538070, +0.40058958184792826), (+1.9056379476987564, +0.83943602247158589), (+1.5726240201901438, +0.16450810248260028), (+1.2868870236579528, +0.14074662919270708), (+1.8266271742527045, +0.36963488532362843), (+1.5831534350228125, +0.26173149061361511), (+1.8673260940272336, +0.43890239333588776), (+1.3145551058824532, +0.25651712241658375), (+1.8062767062477223, +0.27763491020648901E-1), (+1.1749721759974161, +0.77639471257301496), (+1.2193814244948848, +0.24038077532328794), (+1.5344276901444096, +0.21341668980595085), (+1.7358779647990041, +0.60383222107321577), (+1.4021938500420008, +0.41892781001148094), (+1.9378010051452472, +0.88101790521584944), (+1.8834893098143757, +0.84880907447519649), (+1.6992492521621059, +0.98894830273600298), (+1.1216946494227034, +0.33123472495937878), (+1.4788710450950779, +0.20873011384921225), (+1.0432921945350653, +0.14656001231311389), (+1.9836375305191469, +0.24421767918779691), (+1.0954287230492947, +0.64162604631832543E-1), (+1.1117267152176362, +0.61069264675043911), (+1.6434244063724681, +0.48686425030957403), (+1.0217951602127473, +0.96184348852103152), (+1.8019761006842290, +0.59712887428597372E-1), (+1.7366851157254670, +0.76940478598630513E-1), (+1.9387423662323364, +0.33760101291684719E-1), (+1.4985458409138082, +0.16052169981434283)

228

229adat = getFFTR(getFFTF(data)) / size(data)

230adat

231(+1.5595301572292180, +0.78084858314063721), (+1.8415966353195046, +0.33126764059824509E-1), (+1.5474046818316614, +0.70693853994845013), (+1.9916360715032246, +0.84426092444810068E-2), (+1.6942413142225994, +0.23577952398009233), (+1.5283428010624285, +0.52500238029302905E-1), (+1.4565027838252862, +0.58156552943960949), (+1.2571878577159046, +0.13577479625130387), (+1.8042915957534420, +0.70627949771688858), (+1.8280852055082604, +0.63851413042427629), (+1.6827508591670175, +0.32265290612709951), (+1.6680861607467767, +0.73637385418913404E-1), (+1.0678443579329746, +0.27634137325274549), (+1.2553500261876174, +0.13413664545991996), (+1.2759095049342768, +0.18678948229212045), (+1.8546541235538072, +0.40058958184792820), (+1.9056379476987564, +0.83943602247158577), (+1.5726240201901438, +0.16450810248260020), (+1.2868870236579530, +0.14074662919270697), (+1.8266271742527040, +0.36963488532362820), (+1.5831534350228131, +0.26173149061361489), (+1.8673260940272343, +0.43890239333588776), (+1.3145551058824534, +0.25651712241658370), (+1.8062767062477221, +0.27763491020649112E-1), (+1.1749721759974163, +0.77639471257301484), (+1.2193814244948848, +0.24038077532328775), (+1.5344276901444096, +0.21341668980595105), (+1.7358779647990039, +0.60383222107321588), (+1.4021938500420006, +0.41892781001148049), (+1.9378010051452470, +0.88101790521584933), (+1.8834893098143759, +0.84880907447519638), (+1.6992492521621059, +0.98894830273600320), (+1.1216946494227042, +0.33123472495937878), (+1.4788710450950779, +0.20873011384921200), (+1.0432921945350662, +0.14656001231311383), (+1.9836375305191467, +0.24421767918779683), (+1.0954287230492952, +0.64162604631832446E-1), (+1.1117267152176362, +0.61069264675043922), (+1.6434244063724679, +0.48686425030957403), (+1.0217951602127471, +0.96184348852103152), (+1.8019761006842290, +0.59712887428597462E-1), (+1.7366851157254677, +0.76940478598630346E-1), (+1.9387423662323371, +0.33760101291684830E-1), (+1.4985458409138088, +0.16052169981434269)

232reltol = sqrt(epsilon(1._TKG))

233reltol

234+0.14901161193847656E-7

235isClose(data, adat, reltol = reltol)

236T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

237call setAsserted(all(isClose(data, adat, reltol = reltol)))

238

239lenData = getUnifRand(5, 100)

240lenData

241+52

242data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

243data

244(+1.92668983657374548662555725545323950, +0.619696428683560354392071694671141073), (+1.77933630666186316384703785935671090, +0.688605871682851849239273389897700251), (+1.28237211863141444750694253352604567, +0.124948345547896435865389926053773637E-1), (+1.52998677395379987828127322126344963, +0.366917154381254314295158320363008471), (+1.14253640592521542507948936083665089, +0.542290068991219662411785915215342189), (+1.86974844631309469406850929174799062, +0.370079607677681051676978067640607124), (+1.56766678418501178940369381516840706, +0.758501051757001479416248311205573458), (+1.68728730005749507326770323485817580, +0.416110244287449969825785040031460328), (+1.95402869542631394647084664782876973, +0.342481296598398084869762433230248318), (+1.94823239545049920427151238346490691, +0.737844290687348769354757759115415129), (+1.34182691377448526784855711457211579, +0.194351469445088406837313398622083299E-1), (+1.89539129849483127579877567717925687, +0.885333358197035462076192363406184196), (+1.76098349499249861097475207095149619, +0.667925424305112656221939982864637868E-1), (+1.55216620964824196071357724198095397, +0.514154807892516443052961757905382799), (+1.80966562868654114184526056001288947, +0.223433179723704495068116432204237594), (+1.34379580656114440075624053994724451, +0.463626157010792210599343384454454102), (+1.31162030450033412736747623080366334, +0.313842570294347917941070992885124027), (+1.93265733133733586896647362187911110, +0.932026965010665763256936348675419694), (+1.55625523764789024083354279546169539, +0.327405543779151733587165996086591944), (+1.91129249274644536580434756945666515, +0.797793323131338839687680080808355169E-1), (+1.39366364122469739483430818643815466, +0.126827563903946640812899440017023707), (+1.58033870405045359154529987571255891, +0.363085735454309002314478403644875386), (+1.97915482622122897931168708929779403, +0.505721343606312421778841474459421609), (+1.58913719455918775719585388212290980, +0.256447585619646259897655701841276765), (+1.93374078316922181848098085567944441, +0.112886246917764102116701777516721363), (+1.28954235180591018013372869535537989, +0.392565511462526742926065012135309505), (+1.54677195623942736087118363216626195, +0.734877488600631410298112827772015195), (+1.03837790923761477797907580156167288, +0.951591648561893905556473557974286640), (+1.10322460168176713589271776935236088, +0.500032294421779160138010727172825668), (+1.57592301607846396392751120949555792, +0.739033678658703098935048946945585628), (+1.52515018274660436577506146280032017, +0.682937310108123991914790684579124112), (+1.64185789605839795187331569158327356, +0.622028342493627182786963045607341072), (+1.98076106163251585207748119995015891, +0.676585844864769353759287701235481497), (+1.48919185848654083213805155811382330, +0.280908793840870717597842531108024023), (+1.66727712078984637469518154131147960, +0.579125512557168080870045681713988976), (+1.55027621295132359833193138502906518, +0.924921795271795121265379567937673226), (+1.06643137241620968884025577328345304, +0.419218365475630307473760419948263682), (+1.80900430564502961548198990270265639, +0.681365711812730504932859338390383631), (+1.31562638591493725831822865707361004, +0.773563395221594523777024620036120742), (+1.33462391487935521051310284709299526, +0.629050780726805305575072051458007336), (+1.32209115008359494497473482350913071, +0.187196494263686927519666114660602265), (+1.81326389760146177627494611315837142, +0.208299972953388383567658076708860131E-2), (+1.24957320544207582713591936221356435, +0.876202190675872862243445158246973981), (+1.86864109325420813695352125167692609, +0.409589473827257569414644178990985338), (+1.03906123353773345973308934991830176, +0.949221729535278264433327968714981750), (+1.61778349274168837605733232802552493, +0.523152292989226848349990193850704717), (+1.10457541686810935635631180071495629, +0.245025305005707958398366949522735327), (+1.16487726487677398268714106282162329, +0.557831196905276239621174465026657095), (+1.26919530312132857918553095629710189, +0.126570899501642746468785248201185968), (+1.98383936944159230262115525289312065, +0.627595129897880343637337970274369817), (+1.68568887917097638450162512270546280, +0.531972075634550639667386982271630130), (+1.95558942106328479908742353768670509, +0.434727536538401649937373224702210602)

245

246adat = getFFTR(getFFTF(data)) / size(data)

247adat

248(+1.92668983657374548662555725545323950, +0.619696428683560354392071694671140881), (+1.77933630666186316384703785935671148, +0.688605871682851849239273389897700443), (+1.28237211863141444750694253352604586, +0.124948345547896435865389926053776225E-1), (+1.52998677395379987828127322126345040, +0.366917154381254314295158320363008664), (+1.14253640592521542507948936083665128, +0.542290068991219662411785915215341996), (+1.86974844631309469406850929174799139, +0.370079607677681051676978067640607413), (+1.56766678418501178940369381516840667, +0.758501051757001479416248311205573458), (+1.68728730005749507326770323485817503, +0.416110244287449969825785040031460328), (+1.95402869542631394647084664782877011, +0.342481296598398084869762433230248559), (+1.94823239545049920427151238346490729, +0.737844290687348769354757759115415225), (+1.34182691377448526784855711457211656, +0.194351469445088406837313398622084262E-1), (+1.89539129849483127579877567717925687, +0.885333358197035462076192363406184389), (+1.76098349499249861097475207095149735, +0.667925424305112656221939982864639915E-1), (+1.55216620964824196071357724198095320, +0.514154807892516443052961757905382606), (+1.80966562868654114184526056001289043, +0.223433179723704495068116432204237883), (+1.34379580656114440075624053994724451, +0.463626157010792210599343384454454198), (+1.31162030450033412736747623080366431, +0.313842570294347917941070992885124124), (+1.93265733133733586896647362187911148, +0.932026965010665763256936348675419790), (+1.55625523764789024083354279546169655, +0.327405543779151733587165996086592089), (+1.91129249274644536580434756945666477, +0.797793323131338839687680080808353965E-1), (+1.39366364122469739483430818643815428, +0.126827563903946640812899440017023586), (+1.58033870405045359154529987571255929, +0.363085735454309002314478403644875579), (+1.97915482622122897931168708929779422, +0.505721343606312421778841474459421416), (+1.58913719455918775719585388212291018, +0.256447585619646259897655701841276765), (+1.93374078316922181848098085567944499, +0.112886246917764102116701777516721363), (+1.28954235180591018013372869535538066, +0.392565511462526742926065012135309842), (+1.54677195623942736087118363216626118, +0.734877488600631410298112827772015195), (+1.03837790923761477797907580156167365, +0.951591648561893905556473557974286833), (+1.10322460168176713589271776935236107, +0.500032294421779160138010727172825861), (+1.57592301607846396392751120949555850, +0.739033678658703098935048946945585724), (+1.52515018274660436577506146280032017, +0.682937310108123991914790684579124305), (+1.64185789605839795187331569158327414, +0.622028342493627182786963045607341072), (+1.98076106163251585207748119995015891, +0.676585844864769353759287701235481304), (+1.48919185848654083213805155811382253, +0.280908793840870717597842531108023879), (+1.66727712078984637469518154131147979, +0.579125512557168080870045681713989072), (+1.55027621295132359833193138502906499, +0.924921795271795121265379567937673130), (+1.06643137241620968884025577328345342, +0.419218365475630307473760419948263682), (+1.80900430564502961548198990270265658, +0.681365711812730504932859338390383631), (+1.31562638591493725831822865707361158, +0.773563395221594523777024620036121224), (+1.33462391487935521051310284709299449, +0.629050780726805305575072051458006951), (+1.32209115008359494497473482350913225, +0.187196494263686927519666114660602530), (+1.81326389760146177627494611315837142, +0.208299972953388383567658076708871980E-2), (+1.24957320544207582713591936221356512, +0.876202190675872862243445158246974173), (+1.86864109325420813695352125167692628, +0.409589473827257569414644178990985482), (+1.03906123353773345973308934991830215, +0.949221729535278264433327968714981750), (+1.61778349274168837605733232802552474, +0.523152292989226848349990193850704717), (+1.10457541686810935635631180071495572, +0.245025305005707958398366949522735231), (+1.16487726487677398268714106282162387, +0.557831196905276239621174465026657384), (+1.26919530312132857918553095629710227, +0.126570899501642746468785248201185800), (+1.98383936944159230262115525289312142, +0.627595129897880343637337970274370009), (+1.68568887917097638450162512270546319, +0.531972075634550639667386982271630130), (+1.95558942106328479908742353768670605, +0.434727536538401649937373224702210698)

249reltol = sqrt(epsilon(1._TKG))

250reltol

251+0.138777878078144567552953958511352539E-16

252isClose(data, adat, reltol = reltol)

253T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

254call setAsserted(all(isClose(data, adat, reltol = reltol)))

255

256lenData = getUnifRand(5, 100)

257lenData

258+58

259data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

260data

261+1.24601078, +1.09788907, +1.84377480, +1.37818313, +1.51267529, +1.94788170, +1.36048651, +1.56562400, +1.97124171, +1.45563412, +1.35957181, +1.29153132, +1.58967328, +1.80667579, +1.44045365, +1.76630211, +1.61892378, +1.65173149, +1.88321543, +1.15353346, +1.73615503, +1.78628802, +1.42385614, +1.39429975, +1.40086353, +1.84146047, +1.92791390, +1.05447257, +1.81693912, +1.76796114, +1.09848547, +1.06751537, +1.19225001, +1.76412416, +1.30435085, +1.71925712, +1.01657820, +1.51598120, +1.17415571, +1.49267471, +1.52089500, +1.89355326, +1.57654262, +1.75302505, +1.67422855, +1.57757533, +1.21313119, +1.89246976, +1.35924435, +1.64282703, +1.45854855, +1.90072727, +1.74205172, +1.92341423, +1.37981701, +1.70560789, +1.91917408, +1.83440447

262

263adat = getFFTR(getFFTF(data)) / size(data)

264adat

265+1.24601078, +1.09789014, +1.84377456, +1.37818277, +1.51267529, +1.94788206, +1.36048627, +1.56562400, +1.97124135, +1.45563495, +1.35957193, +1.29153156, +1.58967304, +1.80667627, +1.44045341, +1.76630151, +1.61892414, +1.65173185, +1.88321447, +1.15353358, +1.73615491, +1.78628755, +1.42385554, +1.39429951, +1.40086412, +1.84146023, +1.92791271, +1.05447316, +1.81693995, +1.76796234, +1.09848857, +1.06752086, +1.19224894, +1.76412165, +1.30435133, +1.71925867, +1.01657784, +1.51597989, +1.17415631, +1.49267530, +1.52089405, +1.89355195, +1.57654309, +1.75302577, +1.67422771, +1.57757497, +1.21313131, +1.89247036, +1.35924411, +1.64282703, +1.45854843, +1.90072799, +1.74205101, +1.92341387, +1.37981701, +1.70560849, +1.91917384, +1.83440399

266reltol = sqrt(epsilon(1._TKG))

267reltol

268+0.345266977E-3

269isClose(data, adat, reltol = reltol)

270T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

271call setAsserted(all(isClose(data, adat, reltol = reltol)))

272

273lenData = getUnifRand(5, 100)

274lenData

275+56

276data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

277data

278+1.6543311666426121, +1.4276703810886242, +1.7333257647297116, +1.8118511585914576, +1.0972745121463516, +1.6708084906034335, +1.6161970861867707, +1.0914990049528916, +1.6115544151726722, +1.1468772346969445, +1.3321086948224448, +1.0940364006984362, +1.9905948579703987, +1.5576752483523131, +1.1066510988914118, +1.8651905138761158, +1.5958556669789670, +1.4453246335570098, +1.1172476499773536, +1.8182564393981560, +1.5704941987763132, +1.7753846414161272, +1.1406189510555076, +1.8849038194475436, +1.5477306728478077, +1.1253324243686498, +1.5039295990850161, +1.7304706941983232, +1.2382091733760447, +1.3156184883203081, +1.3666460693580342, +1.5955708171175038, +1.3740544674361868, +1.7703784572922394, +1.8994243228331542, +1.2987272206629381, +1.1904236607775422, +1.1053195050663254, +1.2687160173224186, +1.7641853843636617, +1.5107409950073531, +1.4064665662173303, +1.7592949283252892, +1.4154021659691680, +1.9102842394432589, +1.3591082582593836, +1.8202520002935241, +1.1691874638056567, +1.0202370994277268, +1.3573035601976340, +1.9167277986454609, +1.9997167236360993, +1.8152297467677669, +1.1945450852519470, +1.9043336178628389, +1.9893213319979417

279

280adat = getFFTR(getFFTF(data)) / size(data)

281adat

282+1.6543311666426119, +1.4276703810886242, +1.7333257647297116, +1.8118511585914574, +1.0972745121463510, +1.6708084906034328, +1.6161970861867709, +1.0914990049528912, +1.6115544151726717, +1.1468772346969438, +1.3321086948224450, +1.0940364006984358, +1.9905948579703985, +1.5576752483523129, +1.1066510988914122, +1.8651905138761153, +1.5958556669789672, +1.4453246335570100, +1.1172476499773543, +1.8182564393981562, +1.5704941987763135, +1.7753846414161274, +1.1406189510555080, +1.8849038194475440, +1.5477306728478073, +1.1253324243686487, +1.5039295990850157, +1.7304706941983228, +1.2382091733760441, +1.3156184883203075, +1.3666460693580340, +1.5955708171175029, +1.3740544674361863, +1.7703784572922392, +1.8994243228331540, +1.2987272206629377, +1.1904236607775416, +1.1053195050663247, +1.2687160173224183, +1.7641853843636610, +1.5107409950073534, +1.4064665662173303, +1.7592949283252899, +1.4154021659691678, +1.9102842394432593, +1.3591082582593834, +1.8202520002935247, +1.1691874638056572, +1.0202370994277263, +1.3573035601976335, +1.9167277986454609, +1.9997167236360991, +1.8152297467677665, +1.1945450852519468, +1.9043336178628394, +1.9893213319979417

283reltol = sqrt(epsilon(1._TKG))

284reltol

285+0.14901161193847656E-7

286isClose(data, adat, reltol = reltol)

287T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

288call setAsserted(all(isClose(data, adat, reltol = reltol)))

289

290lenData = getUnifRand(5, 100)

291lenData

292+47

293data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

294data

295+1.66032926415803099189633150200087486, +1.29841787233527481142920468865242963, +1.52824783648007113627444600048759809, +1.82590100924546035920536861851941583, +1.18804369306775569898679718139597951, +1.29201877822748702685428098688148397, +1.87821893901739926572899061535142847, +1.08334520183414022947245407138450659, +1.80490105478656591635821393055071803, +1.49091129173473455402584117707477410, +1.17279094388890408092867655411854491, +1.47730469599445934663602110246069554, +1.91756436743273069505718545371601944, +1.61411931902036252098302742785474571, +1.76544096810195578035479398487850141, +1.68784143122999700383956803776247464, +1.13325978526442105824718768531773403, +1.44216654725103888403653037224771233, +1.32847117772901186969340784044368425, +1.23054658979913793986750231596587061, +1.80200426858312106085333607004311943, +1.01837131257141056922804776357700677, +1.05713841732204256881366728551892093, +1.96673341209352816544432736993240262, +1.03047676120025113236197303521956665, +1.73301782908995760929303709707081987, +1.98713871673300099804845205149343574, +1.98025473131121228971878478249595450, +1.67885495631857036388161263519398664, +1.30853786385002456676854268226496304, +1.84979348858293148199167568865693015, +1.72108606535500313000189565264880876, +1.86282796430363376382599246161480267, +1.68418812781352024805403498360256630, +1.62769433707933856912165735852409370, +1.16105838152346567899047994035411407, +1.20673233835948748657647417961609323, +1.97810582775545782158809535272937276, +1.25092383348189893271912092152730936, +1.25814972863697489368068146445346285, +1.28440855852347365964297203605714570, +1.84890038289324596438243136710392104, +1.44448958503539573662460460230365200, +1.88054300553218758924098133055473240, +1.48665608824037976604426690911397870, +1.15587714972454205542275678244062401, +1.98647604272214005211809004376229843

296

297adat = getFFTR(getFFTF(data)) / size(data)

298adat

299+1.66032926415803099189633150200087467, +1.29841787233527481142920468865243021, +1.52824783648007113627444600048759771, +1.82590100924546035920536861851941622, +1.18804369306775569898679718139598008, +1.29201877822748702685428098688148397, +1.87821893901739926572899061535142712, +1.08334520183414022947245407138450602, +1.80490105478656591635821393055071745, +1.49091129173473455402584117707477391, +1.17279094388890408092867655411854433, +1.47730469599445934663602110246069515, +1.91756436743273069505718545371601770, +1.61411931902036252098302742785474513, +1.76544096810195578035479398487850084, +1.68784143122999700383956803776247522, +1.13325978526442105824718768531773423, +1.44216654725103888403653037224771310, +1.32847117772901186969340784044368367, +1.23054658979913793986750231596587003, +1.80200426858312106085333607004311808, +1.01837131257141056922804776357700658, +1.05713841732204256881366728551892016, +1.96673341209352816544432736993240589, +1.03047676120025113236197303521956761, +1.73301782908995760929303709707081987, +1.98713871673300099804845205149343651, +1.98025473131121228971878478249595180, +1.67885495631857036388161263519398702, +1.30853786385002456676854268226496284, +1.84979348858293148199167568865693073, +1.72108606535500313000189565264880915, +1.86282796430363376382599246161480363, +1.68418812781352024805403498360256591, +1.62769433707933856912165735852409351, +1.16105838152346567899047994035411330, +1.20673233835948748657647417961609207, +1.97810582775545782158809535272937160, +1.25092383348189893271912092152730917, +1.25814972863697489368068146445346285, +1.28440855852347365964297203605714551, +1.84890038289324596438243136710391989, +1.44448958503539573662460460230365161, +1.88054300553218758924098133055473259, +1.48665608824037976604426690911397870, +1.15587714972454205542275678244062362, +1.98647604272214005211809004376229939

300reltol = sqrt(epsilon(1._TKG))

301reltol

302+0.138777878078144567552953958511352539E-16

303isClose(data, adat, reltol = reltol)

304T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

305call setAsserted(all(isClose(data, adat, reltol = reltol)))

306

307lenData = getUnifRand(5, 100)

308lenData

309+61

310data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

311data

312(+1.72545135, +0.400444925), (+1.81078565, +0.100200653), (+1.35754490, +0.238043845), (+1.79993331, +0.779503584E-2), (+1.63142300, +0.111223042), (+1.55802321, +0.723135889), (+1.98808694, +0.566564441), (+1.60042262, +0.509221494), (+1.85000479, +0.922260702), (+1.08591175, +0.513101578), (+1.19285107, +0.519933522), (+1.20193994, +0.725371957), (+1.98208809, +0.822030842), (+1.90895772, +0.324368119), (+1.53024745, +0.300109684), (+1.58628154, +0.535033822), (+1.88115180, +0.706670523), (+1.93502843, +0.243251622), (+1.39610374, +0.557826042), (+1.44415975, +0.677857220), (+1.07021940, +0.512912869), (+1.43440497, +0.619936168), (+1.80590999, +0.759675682), (+1.42018557, +0.924601555), (+1.71418309, +0.583609879), (+1.05964112, +0.208347976), (+1.93823838, +0.719442248), (+1.43127918, +0.962768614), (+1.93686604, +0.229469955), (+1.34866762, +0.826849103), (+1.64849436, +0.753138959), (+1.83998251, +0.652874947), (+1.63958931, +0.262748301), (+1.70230699, +0.286688447), (+1.76506138, +0.133074701), (+1.96301198, +0.702387869), (+1.79163694, +0.252112746E-1), (+1.96549463, +0.577133536), (+1.07106423, +0.439797103), (+1.13227272, +0.715867996), (+1.51434636, +0.470470309), (+1.63085651, +0.786512792), (+1.89722991, +0.334850550), (+1.55271840, +0.919782281), (+1.25979114, +0.110155940), (+1.11729312, +0.668196619), (+1.83108974, +0.611615300), (+1.03171492, +0.521425605), (+1.78988528, +0.895240963), (+1.12973666, +0.368874133), (+1.70378041, +0.483311117), (+1.02767229, +0.543308556), (+1.97909117, +0.756278217), (+1.02650499, +0.166803598), (+1.20804441, +0.544320405), (+1.31904864, +0.531446695), (+1.92867541, +0.189275324), (+1.66301799, +0.799621761), (+1.88763309, +0.905429661), (+1.12467337, +0.748638511E-1), (+1.29478180, +0.179340303)

313

314adat = getFFTR(getFFTF(data)) / size(data)

315adat

316(+1.72545326, +0.400445640), (+1.81078517, +0.100200467), (+1.35754490, +0.238043800), (+1.79993284, +0.779502140E-2), (+1.63142335, +0.111222878), (+1.55802262, +0.723135650), (+1.98808706, +0.566564739), (+1.60042262, +0.509221554), (+1.85000467, +0.922260582), (+1.08591163, +0.513101518), (+1.19285107, +0.519933522), (+1.20193958, +0.725372076), (+1.98208821, +0.822030962), (+1.90895796, +0.324368060), (+1.53024733, +0.300109863), (+1.58628190, +0.535033762), (+1.88115191, +0.706670582), (+1.93502891, +0.243251652), (+1.39610398, +0.557826042), (+1.44416022, +0.677857280), (+1.07021976, +0.512912631), (+1.43440557, +0.619936049), (+1.80591023, +0.759675562), (+1.42018580, +0.924601495), (+1.71418369, +0.583609998), (+1.05964100, +0.208347827), (+1.93823886, +0.719442427), (+1.43127966, +0.962768674), (+1.93686652, +0.229469821), (+1.34866762, +0.826849163), (+1.64849460, +0.753138781), (+1.83998275, +0.652874947), (+1.63958919, +0.262748361), (+1.70230770, +0.286688268), (+1.76506162, +0.133074805), (+1.96301234, +0.702387929), (+1.79163682, +0.252111703E-1), (+1.96549499, +0.577133715), (+1.07106471, +0.439797133), (+1.13227296, +0.715867937), (+1.51434684, +0.470470309), (+1.63085663, +0.786512673), (+1.89723015, +0.334850550), (+1.55271876, +0.919782281), (+1.25979149, +0.110155985), (+1.11729348, +0.668196678), (+1.83108997, +0.611615121), (+1.03171492, +0.521425784), (+1.78988540, +0.895240784), (+1.12973702, +0.368874252), (+1.70377994, +0.483311146), (+1.02767241, +0.543308735), (+1.97909081, +0.756278217), (+1.02650511, +0.166803584), (+1.20804453, +0.544320405), (+1.31904888, +0.531446874), (+1.92867470, +0.189275086), (+1.66301823, +0.799621701), (+1.88763261, +0.905429542), (+1.12467360, +0.748637840E-1), (+1.29478145, +0.179340079)

317reltol = sqrt(epsilon(1._TKG))

318reltol

319+0.345266977E-3

320isClose(data, adat, reltol = reltol)

321T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

322call setAsserted(all(isClose(data, adat, reltol = reltol)))

323

324lenData = getUnifRand(5, 100)

325lenData

326+67

327data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

328data

329(+1.5130969671197496, +0.66538376586687686), (+1.3724269912703191, +0.40251645169753592), (+1.6671846851499046, +0.62548372940320984), (+1.7078760938698123, +0.57565761129391968), (+1.0812416686385666, +0.59428647932291168), (+1.9119304844861635, +0.83493169705949666E-1), (+1.2818428219445031, +0.88578585157570588), (+1.5388749407718354, +0.45826254871332728), (+1.3165150022899965, +0.34055874343271852), (+1.5720432233585884, +0.59229137040965141), (+1.2896419117278812, +0.87999966374580996), (+1.3759540918750059, +0.77937920335535038), (+1.1029537752206047, +0.73800746470810907), (+1.4995770995286839, +0.91650710390726942), (+1.9641173387672923, +0.20968383859243733), (+1.7928400889236065, +0.27930273433119301), (+1.1718257976355229, +0.80215879588631656), (+1.6968762113200488, +0.52225130695576227), (+1.9577737340952839, +0.89296241700395096), (+1.2379909493933581, +0.79808972005461110E-1), (+1.1848622274787299, +0.87402964918553516), (+1.8391114439113196, +0.11712511168529272), (+1.5599261933631978, +0.34800999474442851), (+1.5720041149317070, +0.48342904765938555), (+1.8252558593203645, +0.89073304249307583), (+1.1034116161790479, +0.14170828915208233), (+1.1430957213050137, +0.50970971247250862), (+1.4450142632357119, +0.39654249562182808), (+1.8565690758194053, +0.73895639257106471), (+1.8158963688890877, +0.22495503235343095), (+1.5411528600052753, +0.34669964628809324), (+1.1668629557964127, +0.18165538185148988), (+1.0551334266598906, +0.34155725819008442), (+1.0890031317121682, +0.65574289314460421), (+1.5397985085615984, +0.21862167690380663), (+1.3036730368739859, +0.77125481383783245), (+1.8572843600138076, +0.89720112288889786), (+1.9385342493548650, +0.37178660536182684E-1), (+1.7048309903561862, +0.21423299409166652E-1), (+1.0440145832278374, +0.99662266957304846), (+1.9063044851364361, +0.64200585680749755), (+1.4970582177876741, +0.26066937218757513), (+1.9477933354892343, +0.85324907364480784), (+1.1059385490590812, +0.63560156025007863), (+1.1038394045511071, +0.92133382589449686), (+1.0349663701527578, +0.39757560046381879), (+1.2368325112733798, +0.22852708326610283), (+1.9707686613170388, +0.51199363959010835), (+1.2175934017983132, +0.51174696237782169), (+1.5368449945100200, +0.48180989618896863), (+1.3733772260433272, +0.42264859014117451), (+1.9071827956712983, +0.27090677298194343), (+1.8584655757026369, +0.98295775254363293), (+1.8779510205746059, +0.49567328654213549), (+1.0756987372362474, +0.56214024642840676), (+1.3141744250526306, +0.49648506786479374), (+1.5578515006883675, +0.57361406963367123), (+1.0523150039366680, +0.87027408516227756), (+1.2747479841772249, +0.86690520931010551), (+1.5952590755106946, +0.82484221089312748), (+1.9884373707205207, +0.52858492958137060), (+1.2509606027038656, +0.60945659322510726), (+1.9451888499230208, +0.68078379197178229), (+1.3688260377584722, +0.99634710049950503E-1), (+1.1323484312483423, +0.94329459487310197), (+1.0241414092038141, +0.73815590217123050), (+1.6823734471437288, +0.80952172349660279)

330

331adat = getFFTR(getFFTF(data)) / size(data)

332adat

333(+1.5130969671197472, +0.66538376586687609), (+1.3724269912703189, +0.40251645169753597), (+1.6671846851499041, +0.62548372940321029), (+1.7078760938698117, +0.57565761129391957), (+1.0812416686385664, +0.59428647932291179), (+1.9119304844861640, +0.83493169705949763E-1), (+1.2818428219445033, +0.88578585157570600), (+1.5388749407718356, +0.45826254871332744), (+1.3165150022899965, +0.34055874343271841), (+1.5720432233585877, +0.59229137040965163), (+1.2896419117278815, +0.87999966374581007), (+1.3759540918750066, +0.77937920335535005), (+1.1029537752206049, +0.73800746470810952), (+1.4995770995286837, +0.91650710390726942), (+1.9641173387672932, +0.20968383859243736), (+1.7928400889236058, +0.27930273433119296), (+1.1718257976355231, +0.80215879588631700), (+1.6968762113200495, +0.52225130695576216), (+1.9577737340952834, +0.89296241700395140), (+1.2379909493933576, +0.79808972005461068E-1), (+1.1848622274787293, +0.87402964918553527), (+1.8391114439113188, +0.11712511168529281), (+1.5599261933631978, +0.34800999474442845), (+1.5720041149317070, +0.48342904765938560), (+1.8252558593203643, +0.89073304249307617), (+1.1034116161790484, +0.14170828915208261), (+1.1430957213050139, +0.50970971247250874), (+1.4450142632357124, +0.39654249562182847), (+1.8565690758194060, +0.73895639257106494), (+1.8158963688890875, +0.22495503235343092), (+1.5411528600052755, +0.34669964628809330), (+1.1668629557964127, +0.18165538185148997), (+1.0551334266598897, +0.34155725819008448), (+1.0890031317121680, +0.65574289314460432), (+1.5397985085615977, +0.21862167690380649), (+1.3036730368739851, +0.77125481383783256), (+1.8572843600138076, +0.89720112288889797), (+1.9385342493548652, +0.37178660536182510E-1), (+1.7048309903561858, +0.21423299409166516E-1), (+1.0440145832278378, +0.99662266957304879), (+1.9063044851364364, +0.64200585680749789), (+1.4970582177876741, +0.26066937218757524), (+1.9477933354892347, +0.85324907364480795), (+1.1059385490590810, +0.63560156025007897), (+1.1038394045511071, +0.92133382589449697), (+1.0349663701527574, +0.39757560046381873), (+1.2368325112733793, +0.22852708326610291), (+1.9707686613170381, +0.51199363959010824), (+1.2175934017983130, +0.51174696237782158), (+1.5368449945100193, +0.48180989618896902), (+1.3733772260433279, +0.42264859014117417), (+1.9071827956712986, +0.27090677298194382), (+1.8584655757026363, +0.98295775254363316), (+1.8779510205746066, +0.49567328654213560), (+1.0756987372362476, +0.56214024642840654), (+1.3141744250526304, +0.49648506786479407), (+1.5578515006883682, +0.57361406963367079), (+1.0523150039366682, +0.87027408516227778), (+1.2747479841772245, +0.86690520931010562), (+1.5952590755106943, +0.82484221089312748), (+1.9884373707205210, +0.52858492958137082), (+1.2509606027038658, +0.60945659322510748), (+1.9451888499230208, +0.68078379197178251), (+1.3688260377584720, +0.99634710049950642E-1), (+1.1323484312483418, +0.94329459487310208), (+1.0241414092038139, +0.73815590217123084), (+1.6823734471437286, +0.80952172349660312)

334reltol = sqrt(epsilon(1._TKG))

335reltol

336+0.14901161193847656E-7

337isClose(data, adat, reltol = reltol)

338T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

339call setAsserted(all(isClose(data, adat, reltol = reltol)))

340

341lenData = getUnifRand(5, 100)

342lenData

343+40

344data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

345data

346(+1.27631108958632030860823121624468100, +0.925324264873027631512587317492313417), (+1.00317013704564541667678685536779047, +0.224854851274763539698139535862893264), (+1.45855214345377591392869138643033704, +0.578132788103957312565392002355751163), (+1.41496310952878352517290889837234351, +0.472724337414821835862948116154996440), (+1.28499514010092782239005805102818560, +0.340570147694861967059235345086373490), (+1.54838499726779496055711584887008989, +0.972978876338397654797384561685285352), (+1.77738971476612744684073852688087805, +0.558893291814897563326006426328537957), (+1.93221452905197299791387102134222488, +0.460600947243342733339769073108103938), (+1.38128890326707820354211772956525586, +0.558052059831730734614983085981302836), (+1.41464839428710358965619929900327015, +0.776476542191447154844476944961515618), (+1.15375547158767598186394536283965261, +0.183412786015057307505792718126227448), (+1.71210934531806239298809884690806972, +0.846776530719713334160475901858903408), (+1.33166456041077079723044373819018460, +0.680628985317276622156967050642549510), (+1.65859779160137351173634092646661271, +0.849180897360839920300474258325706581), (+1.55481432021031860921872335104823668, +0.991423876083364132228330620226808896), (+1.98152737377390019319454028285925232, +0.775972413886484511806315275587606691), (+1.34983899484628293432824903619138288, +0.765101472258492877435599182619486446), (+1.48388330842572819710136561740398257, +0.719499661259553490257319153238634271E-1), (+1.12613262477506415571639686579208749, +0.378497796514735735819496230048351377), (+1.35349995494136774682798874613065918, +0.504687033302022525015677191695593806), (+1.59561571750504909588014591845728840, +0.706128129377687647888741809108264815), (+1.81800035790741544170058895236596257, +0.812644631460615403122731330333664562), (+1.80517433121449617005617750161833312, +0.568335005412531052385190468304514692), (+1.08792866380329969853024860942020481, +0.987375611448379695669469111431431900), (+1.35642079323303781592358403497722077, +0.725792076109352089194735283465741893), (+1.96132115676184836247133871313130334, +0.432346038916474096685298044912724750), (+1.89631297332237013844415760385327903, +0.754577094406134511349884612162133612), (+1.49825220529512772501082106042199569, +0.588603208842562962510613540576611892), (+1.64187817477480380681225684216071064, +0.590355337204924578608578930370537229), (+1.62914273128400972007771367170168490, +0.120946203538372168614413002305388300), (+1.11568439219520948570281356868245990, +0.223043658893922451346163357302191632), (+1.23035519404243236790026168398664282, +0.160937979919213328719133654547455437), (+1.93260390797473978983652055547851643, +0.848023486707203930253067157282265619), (+1.13789640438795008577785548583301351, +0.754466961752774845036281034292262940), (+1.11375589632857056137822415211000316, +0.301372805640031523235851645811108382), (+1.95860655662236858827697591636894805, +0.841596846669087303942413947016460323), (+1.99401438181971758962603823246318430, +0.785315957683969489732257411454355997), (+1.09498093262583415868505854562408193, +0.543933105432997285802270984288870626), (+1.77515184533619989192790604942947910, +0.535681854632310079819614893995896627), (+1.59256389891212954791341045091652492, +0.932419274009019877472594730854883281)

347

348adat = getFFTR(getFFTF(data)) / size(data)

349adat

350(+1.27631108958632030860823121624468061, +0.925324264873027631512587317492313513), (+1.00317013704564541667678685536779086, +0.224854851274763539698139535862893120), (+1.45855214345377591392869138643033742, +0.578132788103957312565392002355751356), (+1.41496310952878352517290889837234351, +0.472724337414821835862948116154996440), (+1.28499514010092782239005805102818599, +0.340570147694861967059235345086373731), (+1.54838499726779496055711584887008950, +0.972978876338397654797384561685285159), (+1.77738971476612744684073852688087844, +0.558893291814897563326006426328537957), (+1.93221452905197299791387102134222507, +0.460600947243342733339769073108103842), (+1.38128890326707820354211772956525586, +0.558052059831730734614983085981302933), (+1.41464839428710358965619929900327034, +0.776476542191447154844476944961515714), (+1.15375547158767598186394536283965261, +0.183412786015057307505792718126227375), (+1.71210934531806239298809884690806991, +0.846776530719713334160475901858903311), (+1.33166456041077079723044373819018480, +0.680628985317276622156967050642549510), (+1.65859779160137351173634092646661271, +0.849180897360839920300474258325706581), (+1.55481432021031860921872335104823706, +0.991423876083364132228330620226808993), (+1.98152737377390019319454028285925232, +0.775972413886484511806315275587606595), (+1.34983899484628293432824903619138288, +0.765101472258492877435599182619486638), (+1.48388330842572819710136561740398257, +0.719499661259553490257319153238633548E-1), (+1.12613262477506415571639686579208768, +0.378497796514735735819496230048351473), (+1.35349995494136774682798874613065957, +0.504687033302022525015677191695593613), (+1.59561571750504909588014591845728821, +0.706128129377687647888741809108264815), (+1.81800035790741544170058895236596257, +0.812644631460615403122731330333664466), (+1.80517433121449617005617750161833370, +0.568335005412531052385190468304514789), (+1.08792866380329969853024860942020500, +0.987375611448379695669469111431431708), (+1.35642079323303781592358403497722097, +0.725792076109352089194735283465741989), (+1.96132115676184836247133871313130295, +0.432346038916474096685298044912724654), (+1.89631297332237013844415760385327922, +0.754577094406134511349884612162133709), (+1.49825220529512772501082106042199588, +0.588603208842562962510613540576611795), (+1.64187817477480380681225684216071064, +0.590355337204924578608578930370537326), (+1.62914273128400972007771367170168509, +0.120946203538372168614413002305388372), (+1.11568439219520948570281356868246029, +0.223043658893922451346163357302191391), (+1.23035519404243236790026168398664301, +0.160937979919213328719133654547455316), (+1.93260390797473978983652055547851623, +0.848023486707203930253067157282265715), (+1.13789640438795008577785548583301370, +0.754466961752774845036281034292262940), (+1.11375589632857056137822415211000355, +0.301372805640031523235851645811108478), (+1.95860655662236858827697591636894747, +0.841596846669087303942413947016460419), (+1.99401438181971758962603823246318469, +0.785315957683969489732257411454355997), (+1.09498093262583415868505854562408193, +0.543933105432997285802270984288870530), (+1.77515184533619989192790604942947929, +0.535681854632310079819614893995896435), (+1.59256389891212954791341045091652492, +0.932419274009019877472594730854883185)

351reltol = sqrt(epsilon(1._TKG))

352reltol

353+0.138777878078144567552953958511352539E-16

354isClose(data, adat, reltol = reltol)

355T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

356call setAsserted(all(isClose(data, adat, reltol = reltol)))

357

358lenData = getUnifRand(5, 100)

359lenData

360+23

361data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

362data

363+1.18128490, +1.61470103, +1.90253878, +1.64059973, +1.32783985, +1.12984157, +1.27200747, +1.70051789, +1.64847207, +1.69975841, +1.50234127, +1.21416795, +1.55077672, +1.35079253, +1.66019773, +1.10552835, +1.88539469, +1.55626988, +1.08673096, +1.76522470, +1.51377273, +1.47484899, +1.25181544

364

365adat = getFFTR(getFFTF(data)) / size(data)

366adat

367+1.18128490, +1.61470163, +1.90253818, +1.64059961, +1.32783890, +1.12984169, +1.27200663, +1.70051789, +1.64847136, +1.69975889, +1.50234008, +1.21417081, +1.55077779, +1.35079241, +1.66019750, +1.10552859, +1.88539433, +1.55626893, +1.08673108, +1.76522350, +1.51377285, +1.47484851, +1.25181615

368reltol = sqrt(epsilon(1._TKG))

369reltol

370+0.345266977E-3

371isClose(data, adat, reltol = reltol)

372T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

373call setAsserted(all(isClose(data, adat, reltol = reltol)))

374

375lenData = getUnifRand(5, 100)

376lenData

377+37

378data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

379data

380+1.6022340276383966, +1.0041466282755787, +1.7042212885047516, +1.1923865134154994, +1.6251222100213756, +1.0418821903308664, +1.8262973528462130, +1.6037591640643389, +1.5375896936523923, +1.7089339669768280, +1.3356534020018178, +1.0473234051350289, +1.1705925513955127, +1.0696952967907289, +1.7326506326808830, +1.7027540857665855, +1.1765324578503373, +1.4742252633565869, +1.6502898032209998, +1.5999758756077087, +1.0874609452733277, +1.7336125635404174, +1.7401706899686569, +1.6956465147310609, +1.4095536488401610, +1.9072477699363786, +1.1441161635410459, +1.5419979737679381, +1.4698670724026164, +1.3612034320271611, +1.3674765275624108, +1.3819002221196461, +1.1301058620674427, +1.5344659315290110, +1.7050546419185255, +1.7461919683112459, +1.7197349210017334

381

382adat = getFFTR(getFFTF(data)) / size(data)

383adat

384+1.6022340276383966, +1.0041466282755784, +1.7042212885047521, +1.1923865134154996, +1.6251222100213760, +1.0418821903308679, +1.8262973528462132, +1.6037591640643392, +1.5375896936523923, +1.7089339669768280, +1.3356534020018180, +1.0473234051350298, +1.1705925513955129, +1.0696952967907309, +1.7326506326808830, +1.7027540857665833, +1.1765324578503389, +1.4742252633565862, +1.6502898032209996, +1.5999758756077078, +1.0874609452733293, +1.7336125635404167, +1.7401706899686560, +1.6956465147310611, +1.4095536488401628, +1.9072477699363775, +1.1441161635410477, +1.5419979737679379, +1.4698670724026164, +1.3612034320271611, +1.3674765275624106, +1.3819002221196464, +1.1301058620674440, +1.5344659315290119, +1.7050546419185257, +1.7461919683112463, +1.7197349210017330

385reltol = sqrt(epsilon(1._TKG))

386reltol

387+0.14901161193847656E-7

388isClose(data, adat, reltol = reltol)

389T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

390call setAsserted(all(isClose(data, adat, reltol = reltol)))

391

392lenData = getUnifRand(5, 100)

393lenData

394+76

395data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

396data

397+1.89832495168138515327265352090355373, +1.60514033016926710020942651970465726, +1.76535119273899920963423611394199362, +1.48941227447024314761388077793446574, +1.55552700530089007886143744806603072, +1.15307236888418537981610502688988833, +1.59524130133614449072693566736956208, +1.98643518496687619472179553081182897, +1.67157839058191909574455796468052890, +1.84632927563225425696286913680404509, +1.77505383688714121181883277332573165, +1.01791732408338847891245985191058209, +1.03031600888400987527809524780927913, +1.36368547546421169699586314695786413, +1.04805040968112421383577325259341874, +1.06489192877647729679515669908427012, +1.51017983476074353810431405272227340, +1.43682115055139471119421965833620190, +1.30109299122219490995385524721193821, +1.59707265808227650472500494000206558, +1.65171728123229400916171825621813379, +1.74589562011410885276708332543681878, +1.20859211707569620106245853353426097, +1.05416058754705826714941158024201220, +1.72695226936393130416384387310241399, +1.42932535279437533727628833663588037, +1.66865004600658830211031873992103543, +1.13751627780081574286628150940465450, +1.80462909267687943640233824122160036, +1.83371447189357375788166560238538613, +1.45224931817378567644907683183048203, +1.86895458075618338187495083309667444, +1.98422256032239901483579685284741703, +1.32360203099555821066623743527106565, +1.45564285904882841953726672228627181, +1.80967199116532871287928887535010599, +1.90072457950789888062758007384431319, +1.16449370870222296872182694713601216, +1.26653394757789952952533860519184514, +1.30850290297143247183774895925274224, +1.56932208809166917975896906988527491, +1.00961619434750442647079768600524202, +1.06066276413911271220875854671217823, +1.42522254001182588168891223483293709, +1.49210610184480040144714197715833257, +1.30679118955917902937968675482362428, +1.81655887668605176602587131815896586, +1.37812265139894911333963992634135995, +1.13026174301749846734418684657187116, +1.50769689286670940417907799393914637, +1.79627543552091946876135042071025282, +1.03205846211445535815145801045932208, +1.21584119619023617847954170606705057, +1.09648347345471593525125922935192818, +1.09600310174947827919210011238494942, +1.29130783963245698179346772256740827, +1.21870179086957621528036370035096103, +1.55878008901017859991440295064925747, +1.42481051071144495745599333081906608, +1.68091765469137191809936547791379755, +1.74944145709793657542503092279960435, +1.43176881792923690114166789956595335, +1.06138377829689248766294375370615334, +1.31067355848530999204446128684797381, +1.70085632472650334676785331551539843, +1.85042371780482897794784330435412637, +1.69299402817608964530413191710156135, +1.48020118776436847225856383486007166, +1.89914029364896314845900165116711017, +1.49605748561502536369135601559316087, +1.92573445309339162686312187603812271, +1.94135776794844898434310045781879799, +1.15582879926293179120502665449156602, +1.24343656602902417207775955346278646, +1.79105784453809639030927297433411845, +1.30643548170531533821198583845716515

398

399adat = getFFTR(getFFTF(data)) / size(data)

400adat

401+1.89832495168138515327265352090355315, +1.60514033016926710020942651970465669, +1.76535119273899920963423611394199304, +1.48941227447024314761388077793446516, +1.55552700530089007886143744806603110, +1.15307236888418537981610502688988756, +1.59524130133614449072693566736956208, +1.98643518496687619472179553081182877, +1.67157839058191909574455796468052948, +1.84632927563225425696286913680404586, +1.77505383688714121181883277332573261, +1.01791732408338847891245985191058267, +1.03031600888400987527809524780927855, +1.36368547546421169699586314695786375, +1.04805040968112421383577325259341816, +1.06489192877647729679515669908426973, +1.51017983476074353810431405272227417, +1.43682115055139471119421965833620209, +1.30109299122219490995385524721193898, +1.59707265808227650472500494000206712, +1.65171728123229400916171825621813436, +1.74589562011410885276708332543681936, +1.20859211707569620106245853353426059, +1.05416058754705826714941158024201143, +1.72695226936393130416384387310241437, +1.42932535279437533727628833663588095, +1.66865004600658830211031873992103697, +1.13751627780081574286628150940465450, +1.80462909267687943640233824122160074, +1.83371447189357375788166560238538728, +1.45224931817378567644907683183048241, +1.86895458075618338187495083309667559, +1.98422256032239901483579685284741895, +1.32360203099555821066623743527106681, +1.45564285904882841953726672228627297, +1.80967199116532871287928887535010830, +1.90072457950789888062758007384431184, +1.16449370870222296872182694713601005, +1.26653394757789952952533860519184340, +1.30850290297143247183774895925273877, +1.56932208809166917975896906988527183, +1.00961619434750442647079768600523913, +1.06066276413911271220875854671217534, +1.42522254001182588168891223483293516, +1.49210610184480040144714197715833449, +1.30679118955917902937968675482362582, +1.81655887668605176602587131815896817, +1.37812265139894911333963992634136169, +1.13026174301749846734418684657187058, +1.50769689286670940417907799393914714, +1.79627543552091946876135042071025474, +1.03205846211445535815145801045932112, +1.21584119619023617847954170606705076, +1.09648347345471593525125922935192857, +1.09600310174947827919210011238494903, +1.29130783963245698179346772256740923, +1.21870179086957621528036370035096083, +1.55878008901017859991440295064925766, +1.42481051071144495745599333081906685, +1.68091765469137191809936547791379832, +1.74944145709793657542503092279960569, +1.43176881792923690114166789956595373, +1.06138377829689248766294375370615315, +1.31067355848530999204446128684797420, +1.70085632472650334676785331551539843, +1.85042371780482897794784330435412676, +1.69299402817608964530413191710156193, +1.48020118776436847225856383486007147, +1.89914029364896314845900165116711074, +1.49605748561502536369135601559316107, +1.92573445309339162686312187603812310, +1.94135776794844898434310045781879876, +1.15582879926293179120502665449156602, +1.24343656602902417207775955346278589, +1.79105784453809639030927297433411864, +1.30643548170531533821198583845716457

402reltol = sqrt(epsilon(1._TKG))

403reltol

404+0.138777878078144567552953958511352539E-16

405isClose(data, adat, reltol = reltol)

406T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

407call setAsserted(all(isClose(data, adat, reltol = reltol)))

408

409lenData = getUnifRand(5, 100)

410lenData

411+53

412data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

413data

414(+1.74826694, +0.171034396), (+1.47767794, +0.594860315E-2), (+1.94142640, +0.392954946E-1), (+1.27516663, +0.366110682), (+1.74806380, +0.866822064), (+1.21891642, +0.335002542E-1), (+1.08217871, +0.560239613), (+1.63721716, +0.433830619), (+1.77446842, +0.718720734), (+1.99781156, +0.121844471), (+1.28254330, +0.365933537), (+1.95928192, +0.646162629), (+1.95133030, +0.351936579), (+1.41658270, +0.183699727), (+1.38004017, +0.143541098E-1), (+1.61190021, +0.611869335), (+1.97929537, +0.308590055), (+1.30308056, +0.753283203), (+1.80759931, +0.787619889), (+1.48044467, +0.492414713), (+1.50197482, +0.346735954), (+1.76536679, +0.998036265), (+1.99666214, +0.759383738), (+1.50727105, +0.476018250), (+1.83481419, +0.384154081), (+1.31295466, +0.484317541E-1), (+1.44922996, +0.330877304E-2), (+1.64993834, +0.570812821), (+1.20453191, +0.740066528), (+1.47608304, +0.224509716), (+1.21186852, +0.630475700), (+1.10054767, +0.401857078), (+1.30958366, +0.179764152), (+1.39854789, +0.446661294), (+1.69467664, +0.509500146), (+1.25070024, +0.785903752), (+1.36531842, +0.492769480), (+1.25024092, +0.441083789), (+1.78641081, +0.676754355), (+1.41446137, +0.754726708), (+1.89565969, +0.406993210), (+1.90613055, +0.871069074), (+1.23225117, +0.851071954), (+1.05168056, +0.543032885E-1), (+1.39062059, +0.170093775E-2), (+1.62555528, +0.692089796), (+1.40578890, +0.816474617), (+1.93098211, +0.451452136E-1), (+1.82925773, +0.499283969), (+1.87874842, +0.389646709), (+1.43679476, +0.318228841), (+1.25818992, +0.976284504), (+1.74360013, +0.297311842)

415

416adat = getFFTR(getFFTF(data)) / size(data)

417adat

418(+1.74827135, +0.171035662), (+1.47767735, +0.594844436E-2), (+1.94142628, +0.392953418E-1), (+1.27516592, +0.366110533), (+1.74806297, +0.866822004), (+1.21891618, +0.335002206E-1), (+1.08217835, +0.560239553), (+1.63721716, +0.433830649), (+1.77446842, +0.718720555), (+1.99781132, +0.121844471), (+1.28254271, +0.365933537), (+1.95928180, +0.646162570), (+1.95133007, +0.351936668), (+1.41658247, +0.183699727), (+1.38004017, +0.143541656E-1), (+1.61190021, +0.611869156), (+1.97929513, +0.308590084), (+1.30308020, +0.753283083), (+1.80759895, +0.787619829), (+1.48044491, +0.492414773), (+1.50197458, +0.346736103), (+1.76536691, +0.998036265), (+1.99666226, +0.759383857), (+1.50727093, +0.476018250), (+1.83481443, +0.384154171), (+1.31295490, +0.484318659E-1), (+1.44923079, +0.330916001E-2), (+1.64993918, +0.570813000), (+1.20453215, +0.740066528), (+1.47608340, +0.224509656), (+1.21186852, +0.630475879), (+1.10054779, +0.401857167), (+1.30958366, +0.179764301), (+1.39854789, +0.446661532), (+1.69467676, +0.509500146), (+1.25070000, +0.785903811), (+1.36531818, +0.492769450), (+1.25024080, +0.441083729), (+1.78641069, +0.676754296), (+1.41446137, +0.754726648), (+1.89565957, +0.406993151), (+1.90613043, +0.871069133), (+1.23225117, +0.851072013), (+1.05167997, +0.543032065E-1), (+1.39062035, +0.170089165E-2), (+1.62555540, +0.692089796), (+1.40578878, +0.816474497), (+1.93098164, +0.451450720E-1), (+1.82925737, +0.499283999), (+1.87874794, +0.389646560), (+1.43679392, +0.318228811), (+1.25818980, +0.976284325), (+1.74359953, +0.297311574)

419reltol = sqrt(epsilon(1._TKG))

420reltol

421+0.345266977E-3

422isClose(data, adat, reltol = reltol)

423T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

424call setAsserted(all(isClose(data, adat, reltol = reltol)))

425

426lenData = getUnifRand(5, 100)

427lenData

428+99

429data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

430data

431(+1.6218696744706764, +0.36365796790394977), (+1.2296696320588136, +0.62701859746331801), (+1.4484859166236081, +0.48853661633070111), (+1.5757154136766776, +0.50954107323143427), (+1.6488430216756724, +0.56518646790619342), (+1.3866855467168020, +0.33716732130073979E-1), (+1.6720656118336228, +0.46337620202440966), (+1.2267110765859135, +0.96825807876147196), (+1.0560450240482444, +0.74667336184054667), (+1.4021516155387013, +0.18467491198113739), (+1.6018541657951693, +0.39141765840049347), (+1.5379064820058039, +0.97250510248627708), (+1.1264120303184271, +0.49899850413806723), (+1.0440747021154806, +0.78278508928236246), (+1.9503615951604161, +0.73136470447934920), (+1.8971873283752028, +0.94697383847059013), (+1.2091493251429375, +0.24361551802620218), (+1.9694475024065974, +0.35275992481939944), (+1.7518719785493309, +0.45187819164281762), (+1.2898846022611457, +0.30104491981604808E-1), (+1.8849270200039145, +0.83201698291178516), (+1.5449282992177102, +0.79478595311778755), (+1.8111698735193373, +0.13119780335338971), (+1.0358209340806239, +0.37599793494814160), (+1.0466122636474400, +0.83203273512035270), (+1.9346321629718073, +0.69969600685401423), (+1.1143321577310938, +0.85257338091100976), (+1.1288430681491870, +0.19268659553972167E-1), (+1.3219322694712070, +0.68271811360547785), (+1.7220605451491191, +0.79386184708912411), (+1.1888640818080285, +0.49855662023223435), (+1.9539415520160488, +0.28158823458381010), (+1.2309500411036578, +0.42280585248107705), (+1.2927231502985179, +0.75642875482210403), (+1.8918504985051805, +0.25840263917699113E-2), (+1.2546329956188176, +0.83401126823451444), (+1.8414256486073626, +0.56122582941059251), (+1.6900050563577047, +0.77374669842969801), (+1.7822557965113357, +0.67366978093537011), (+1.1046388492546215, +0.80339626591029190), (+1.2588563714513277, +0.18080647350098900), (+1.3420202714157003, +0.93862429347130527), (+1.6743612016147340, +0.16193155553553018), (+1.7273547854269751, +0.25956879190444315), (+1.7454640711372251, +0.71246889949142223), (+1.3731603311271003, +0.70049947116902422), (+1.1876688588270352, +0.81565281795864197E-1), (+1.8540904223676744, +0.79005851433670948), (+1.0623342877478530, +0.39178419273831266), (+1.8530489359166467, +0.50587722274808777), (+1.1708489758162695, +0.39707994052170870), (+1.8581946921714294, +0.92249247664141532), (+1.9337076902540979, +0.15197189249555687), (+1.0746050265390887, +0.11224962367129410), (+1.8340489338868933, +0.82437910169595763), (+1.1998915527748237, +0.70355229605344916), (+1.5026936821254515, +0.43673276702339114E-1), (+1.4060795725087631, +0.39637561482565031E-1), (+1.4329448140677203, +0.81187618163132058), (+1.0143716438637846, +0.41334261554998997), (+1.2552684804284111, +0.70074346645965124), (+1.2926437329225431, +0.97481322831761308), (+1.7919906081382924, +0.59673927887723544), (+1.8808719301232557, +0.14548467721238734), (+1.5470502609073660, +0.34806125080547867), (+1.9055088032538912, +0.86952590287092701), (+1.5971748362655753, +0.27957850185717448), (+1.3464346914078966, +0.71479722261181111), (+1.0441160376515612, +0.76937559975305414), (+1.8774659547604839, +0.79961497478847987), (+1.1733269426696444, +0.99131191368810245), (+1.1955931832670865, +0.33452348830740009), (+1.6754756872358230, +0.88565631905168429), (+1.8306902004832031, +0.86249921819646524E-1), (+1.1557777528098265, +0.90240531923573231), (+1.3226217157746456, +0.51625748951338624), (+1.7285386522757857, +0.91607249519040646E-1), (+1.6931598503740859, +0.14874714434392833), (+1.9690555258720150, +0.34673308994267105), (+1.4978185302401599, +0.64649146091834220), (+1.9139939768570509, +0.28655268861442251), (+1.7439999818477452, +0.64346978435885327E-1), (+1.0692403281514551, +0.26037374182780149), (+1.8788984097625436, +0.71112981203210779), (+1.4026341992916818, +0.61015615582446714), (+1.0834651738505567, +0.91923485077455180E-1), (+1.1870246954637920, +0.71580439737972690), (+1.9583314287419036, +0.97766100743761530), (+1.1725301480825923, +0.62646724648122853), (+1.8180057434699215, +0.25415370450448227), (+1.8062737340265662, +0.90912769518360803E-1), (+1.3642368758742380, +0.34345831430095608), (+1.8713767354498652, +0.12582213959548250), (+1.0349548609847721, +0.53025771638227692), (+1.6870225313311322, +0.71036683113754706), (+1.9024194948260831, +0.83903603663400517), (+1.8497865169195715, +0.74614998042033898), (+1.5473129649650641, +0.32994152109372077), (+1.3617428138324490, +0.34815733620986522)

432

433adat = getFFTR(getFFTF(data)) / size(data)

434adat

435(+1.6218696744706771, +0.36365796790395011), (+1.2296696320588130, +0.62701859746331767), (+1.4484859166236084, +0.48853661633070100), (+1.5757154136766776, +0.50954107323143438), (+1.6488430216756722, +0.56518646790619353), (+1.3866855467168013, +0.33716732130073694E-1), (+1.6720656118336226, +0.46337620202440927), (+1.2267110765859137, +0.96825807876147219), (+1.0560450240482444, +0.74667336184054611), (+1.4021516155387008, +0.18467491198113731), (+1.6018541657951686, +0.39141765840049347), (+1.5379064820058048, +0.97250510248627731), (+1.1264120303184266, +0.49899850413806707), (+1.0440747021154801, +0.78278508928236223), (+1.9503615951604159, +0.73136470447934931), (+1.8971873283752030, +0.94697383847059025), (+1.2091493251429373, +0.24361551802620204), (+1.9694475024065963, +0.35275992481939950), (+1.7518719785493311, +0.45187819164281762), (+1.2898846022611459, +0.30104491981605076E-1), (+1.8849270200039137, +0.83201698291178494), (+1.5449282992177100, +0.79478595311778710), (+1.8111698735193384, +0.13119780335339015), (+1.0358209340806233, +0.37599793494814115), (+1.0466122636474400, +0.83203273512035258), (+1.9346321629718073, +0.69969600685401434), (+1.1143321577310936, +0.85257338091100976), (+1.1288430681491866, +0.19268659553972108E-1), (+1.3219322694712066, +0.68271811360547785), (+1.7220605451491189, +0.79386184708912411), (+1.1888640818080287, +0.49855662023223429), (+1.9539415520160479, +0.28158823458380999), (+1.2309500411036576, +0.42280585248107694), (+1.2927231502985186, +0.75642875482210392), (+1.8918504985051805, +0.25840263917698229E-2), (+1.2546329956188169, +0.83401126823451410), (+1.8414256486073626, +0.56122582941059251), (+1.6900050563577045, +0.77374669842969801), (+1.7822557965113348, +0.67366978093537000), (+1.1046388492546215, +0.80339626591029167), (+1.2588563714513272, +0.18080647350098902), (+1.3420202714157006, +0.93862429347130494), (+1.6743612016147340, +0.16193155553552982), (+1.7273547854269748, +0.25956879190444293), (+1.7454640711372258, +0.71246889949142256), (+1.3731603311271003, +0.70049947116902400), (+1.1876688588270352, +0.81565281795864170E-1), (+1.8540904223676742, +0.79005851433670926), (+1.0623342877478528, +0.39178419273831278), (+1.8530489359166460, +0.50587722274808755), (+1.1708489758162688, +0.39707994052170853), (+1.8581946921714294, +0.92249247664141509), (+1.9337076902540984, +0.15197189249555709), (+1.0746050265390883, +0.11224962367129399), (+1.8340489338868928, +0.82437910169595718), (+1.1998915527748248, +0.70355229605344938), (+1.5026936821254508, +0.43673276702338941E-1), (+1.4060795725087627, +0.39637561482564830E-1), (+1.4329448140677201, +0.81187618163132069), (+1.0143716438637842, +0.41334261554998980), (+1.2552684804284107, +0.70074346645965102), (+1.2926437329225429, +0.97481322831761286), (+1.7919906081382919, +0.59673927887723532), (+1.8808719301232557, +0.14548467721238750), (+1.5470502609073655, +0.34806125080547867), (+1.9055088032538905, +0.86952590287092679), (+1.5971748362655764, +0.27957850185717475), (+1.3464346914078957, +0.71479722261181067), (+1.0441160376515608, +0.76937559975305370), (+1.8774659547604842, +0.79961497478847943), (+1.1733269426696449, +0.99131191368810256), (+1.1955931832670859, +0.33452348830740003), (+1.6754756872358232, +0.88565631905168396), (+1.8306902004832029, +0.86249921819646719E-1), (+1.1557777528098265, +0.90240531923573253), (+1.3226217157746454, +0.51625748951338601), (+1.7285386522757848, +0.91607249519040659E-1), (+1.6931598503740866, +0.14874714434392849), (+1.9690555258720146, +0.34673308994267071), (+1.4978185302401603, +0.64649146091834198), (+1.9139939768570502, +0.28655268861442273), (+1.7439999818477450, +0.64346978435885230E-1), (+1.0692403281514546, +0.26037374182780149), (+1.8788984097625425, +0.71112981203210746), (+1.4026341992916822, +0.61015615582446714), (+1.0834651738505570, +0.91923485077455319E-1), (+1.1870246954637913, +0.71580439737972656), (+1.9583314287419031, +0.97766100743761497), (+1.1725301480825934, +0.62646724648122887), (+1.8180057434699206, +0.25415370450448233), (+1.8062737340265660, +0.90912769518360484E-1), (+1.3642368758742378, +0.34345831430095619), (+1.8713767354498652, +0.12582213959548247), (+1.0349548609847719, +0.53025771638227681), (+1.6870225313311313, +0.71036683113754684), (+1.9024194948260826, +0.83903603663400494), (+1.8497865169195720, +0.74614998042033875), (+1.5473129649650641, +0.32994152109372077), (+1.3617428138324486, +0.34815733620986500)

436reltol = sqrt(epsilon(1._TKG))

437reltol

438+0.14901161193847656E-7

439isClose(data, adat, reltol = reltol)

440T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

441call setAsserted(all(isClose(data, adat, reltol = reltol)))

442

443lenData = getUnifRand(5, 100)

444lenData

445+60

446data = 1._TKG + getUnifRand((0._TKG, 0._TKG), (1._TKG, 1._TKG), lenData)

447data

448(+1.32083886728232002570188889980490507, +0.196102427457624420955196439800387637E-2), (+1.70889976648521283479905203100393812, +0.561708231528996479230584097825555994), (+1.13216253748754321974061449228611331, +0.193725736078886822867456309858299055), (+1.81522877277682315602158266463962578, +0.754229215445000883437339427058559151), (+1.28721292812647828340429023067987838, +0.971983045883567159097680691197331248), (+1.55617263495370911050147195044087303, +0.401221115825976925994846684367228428), (+1.40468470202026204460748153865385003, +0.263742129704290871666480485351437717), (+1.48383151695094320916208714184509422, +0.547856869429555293358634459899168455), (+1.57843829147659624725082211064027766, +0.338496963144113276749116445424331858), (+1.83670398721882377832343813062545463, +0.263746319052861428653517180980315960), (+1.00770452426263057081658355595717519, +0.547951849680487524017319473915176140), (+1.30318867064086588483900718107971603, +0.901808086315212890956319189182963935), (+1.58339436129836385846911515535416542, +0.310421839713091716579063816921481254), (+1.36697728555903783928659014739188613, +0.745807631648990691368149329007828575), (+1.44659193502089235323431340500220664, +0.622927672968932862693713344965182035), (+1.85611293271452768136026938399560962, +0.896076823609033162426135229548010238), (+1.57414946734677227903853259662242725, +0.847558089583051113282729696367393346), (+1.16653002322389179444085297096154264, +0.283483591880251762669832732153153124), (+1.20515505904896528860700899905188969, +0.481510253685508004798194081315775482), (+1.49848644500908718075210311053734968, +0.103223190644171633075734005146639023), (+1.49653018907804051405041408354003046, +0.236323628283979321049202512290296339), (+1.85703357027490632327939391168907423, +0.644936121432658546475262002102380357), (+1.72035804896261182178295974128360539, +0.514537659391501964354684769296839778), (+1.29528558263874992023537786585465170, +0.879452663403422204971488682706049308), (+1.64889449595689865012928831845465521, +0.721543022704224797606863369095187536), (+1.32503255091860018762606793858090804, +0.565541264308486745842064068230481690), (+1.46622346104273959623582334681383698, +0.251971025047357105747489392830197512E-1), (+1.88047106952224257091367412142250096, +0.676789993662192121396515111024422252), (+1.42677073588886813586474302741084014, +0.592030602980161323880709657049484648), (+1.53362818192866707712499044689038557, +0.756786657886629506539148678061322636), (+1.56396430767135681546300674295371610, +0.677143218101523695308600351443453787), (+1.78389107700995179111722946481679297, +0.990245040555471251959717402553767737), (+1.64557966135365224079732940947824064, +0.997409170798929673431566617227400666), (+1.15709460762978276383542351078447549, +0.356344079894527062186411901064650878E-1), (+1.62485206777140512712097574561810060, +0.144583752413740955242421035864207135), (+1.62260724959672162536470582850166111, +0.100485085054970607622062004158174390), (+1.32460196545987530618303852959816488, +0.666867223155407570659615631141627044), (+1.10893603287772906945407317740708034, +0.517580301270675019565532337889362885E-1), (+1.65328669490429253761662661714523157, +0.767609856121945791544010522967024975), (+1.61255411615696466636855738463856163, +0.919259461963438728663236346388688700), (+1.87911138195985900203550228547553554, +0.496308347255801845758343646022650930), (+1.15116860639750435497884645972515464, +0.209303369127677685844710887104099359), (+1.06718093446945683282282453482991468, +0.922810177129958723265900262815643401), (+1.96025664063469648161305895902539202, +0.282846380093717209332397076557951224E-1), (+1.01500932008809289711203120155930780, +0.738013811847288104666424177764721362), (+1.45843758960074008030367405494306929, +0.991857966027015235602792633841485282), (+1.17481934848302217694958956880247538, +0.327973722264968273765813025524868816), (+1.44939250332203332871138815357049092, +0.971315210019602627867692956940739168), (+1.33049491633521339117357733579179133, +0.625878493801476851038300703677360933), (+1.61908919472836585330236835048704761, +0.967012650957795766386479914242047698), (+1.80811259020695157237962774328553999, +0.570074190760505866805020760794189491), (+1.99813141352093349525139425096870697, +0.685821534031557334264205162369181650), (+1.42648935466163360752983147204197642, +0.533165940556792706170618481829771513), (+1.46349427811352197622834133058651115, +0.694120847744561752517036159815135007), (+1.26668332085542600326604415826213355, +0.803991982737111885303281973258555548), (+1.74966693596585060546601393902348590, +0.370652600723598912045441999645404328), (+1.90363216927129015638037912401115066, +0.853847411810981147868077249750912710), (+1.92480245747968354308043848047516416, +0.252464403080763151390889469514582719), (+1.24397795875680627825378692767738232, +0.780850153933131453964893178246078403E-1), (+1.13799706740700020572421999748948245, +0.338015848630631324952407081101132677)

449

450adat = getFFTR(getFFTF(data)) / size(data)

451adat

452(+1.32083886728232002570188889980490545, +0.196102427457624420955196439800378647E-2), (+1.70889976648521283479905203100393812, +0.561708231528996479230584097825555994), (+1.13216253748754321974061449228611331, +0.193725736078886822867456309858298959), (+1.81522877277682315602158266463962597, +0.754229215445000883437339427058559055), (+1.28721292812647828340429023067987799, +0.971983045883567159097680691197331151), (+1.55617263495370911050147195044087264, +0.401221115825976925994846684367228331), (+1.40468470202026204460748153865385003, +0.263742129704290871666480485351437765), (+1.48383151695094320916208714184509403, +0.547856869429555293358634459899168359), (+1.57843829147659624725082211064027746, +0.338496963144113276749116445424331858), (+1.83670398721882377832343813062545424, +0.263746319052861428653517180980316056), (+1.00770452426263057081658355595717538, +0.547951849680487524017319473915176140), (+1.30318867064086588483900718107971622, +0.901808086315212890956319189182964128), (+1.58339436129836385846911515535416561, +0.310421839713091716579063816921481206), (+1.36697728555903783928659014739188613, +0.745807631648990691368149329007828575), (+1.44659193502089235323431340500220644, +0.622927672968932862693713344965182227), (+1.85611293271452768136026938399560924, +0.896076823609033162426135229548010046), (+1.57414946734677227903853259662242725, +0.847558089583051113282729696367393346), (+1.16653002322389179444085297096154245, +0.283483591880251762669832732153153076), (+1.20515505904896528860700899905188988, +0.481510253685508004798194081315775482), (+1.49848644500908718075210311053734910, +0.103223190644171633075734005146638999), (+1.49653018907804051405041408354003027, +0.236323628283979321049202512290296363), (+1.85703357027490632327939391168907423, +0.644936121432658546475262002102380357), (+1.72035804896261182178295974128360578, +0.514537659391501964354684769296839874), (+1.29528558263874992023537786585465189, +0.879452663403422204971488682706049212), (+1.64889449595689865012928831845465541, +0.721543022704224797606863369095187536), (+1.32503255091860018762606793858090785, +0.565541264308486745842064068230481690), (+1.46622346104273959623582334681383698, +0.251971025047357105747489392830198596E-1), (+1.88047106952224257091367412142250077, +0.676789993662192121396515111024422155), (+1.42677073588886813586474302741083995, +0.592030602980161323880709657049484552), (+1.53362818192866707712499044689038518, +0.756786657886629506539148678061322829), (+1.56396430767135681546300674295371610, +0.677143218101523695308600351443453787), (+1.78389107700995179111722946481679278, +0.990245040555471251959717402553767737), (+1.64557966135365224079732940947824045, +0.997409170798929673431566617227400666), (+1.15709460762978276383542351078447530, +0.356344079894527062186411901064650878E-1), (+1.62485206777140512712097574561810060, +0.144583752413740955242421035864207183), (+1.62260724959672162536470582850166072, +0.100485085054970607622062004158174246), (+1.32460196545987530618303852959816508, +0.666867223155407570659615631141626948), (+1.10893603287772906945407317740707995, +0.517580301270675019565532337889362946E-1), (+1.65328669490429253761662661714523157, +0.767609856121945791544010522967025072), (+1.61255411615696466636855738463856125, +0.919259461963438728663236346388688700), (+1.87911138195985900203550228547553554, +0.496308347255801845758343646022650834), (+1.15116860639750435497884645972515483, +0.209303369127677685844710887104099407), (+1.06718093446945683282282453482991487, +0.922810177129958723265900262815643497), (+1.96025664063469648161305895902539202, +0.282846380093717209332397076557950833E-1), (+1.01500932008809289711203120155930780, +0.738013811847288104666424177764721458), (+1.45843758960074008030367405494306909, +0.991857966027015235602792633841485089), (+1.17481934848302217694958956880247538, +0.327973722264968273765813025524868960), (+1.44939250332203332871138815357049092, +0.971315210019602627867692956940739072), (+1.33049491633521339117357733579179171, +0.625878493801476851038300703677360933), (+1.61908919472836585330236835048704703, +0.967012650957795766386479914242047698), (+1.80811259020695157237962774328553999, +0.570074190760505866805020760794189491), (+1.99813141352093349525139425096870658, +0.685821534031557334264205162369181650), (+1.42648935466163360752983147204197662, +0.533165940556792706170618481829771513), (+1.46349427811352197622834133058651134, +0.694120847744561752517036159815134911), (+1.26668332085542600326604415826213374, +0.803991982737111885303281973258555645), (+1.74966693596585060546601393902348571, +0.370652600723598912045441999645404232), (+1.90363216927129015638037912401115066, +0.853847411810981147868077249750912806), (+1.92480245747968354308043848047516397, +0.252464403080763151390889469514582671), (+1.24397795875680627825378692767738251, +0.780850153933131453964893178246079847E-1), (+1.13799706740700020572421999748948226, +0.338015848630631324952407081101132773)

453reltol = sqrt(epsilon(1._TKG))

454reltol

455+0.138777878078144567552953958511352539E-16

456isClose(data, adat, reltol = reltol)

457T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

458call setAsserted(all(isClose(data, adat, reltol = reltol)))

459

460lenData = getUnifRand(5, 100)

461lenData

462+64

463data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

464data

465+1.77872014, +1.99383724, +1.31840658, +1.15132105, +1.11332083, +1.67639208, +1.02044761, +1.96374726, +1.48225689, +1.33696520, +1.79447198, +1.36099935, +1.91646123, +1.68929052, +1.43697309, +1.14321673, +1.58884883, +1.60564375, +1.27022600, +1.95489514, +1.14600551, +1.48850727, +1.23601031, +1.90985656, +1.92535877, +1.93595171, +1.91236329, +1.43223047, +1.09946060, +1.29791546, +1.61555052, +1.37773633, +1.61022949, +1.25531316, +1.75815868, +1.49250805, +1.10163307, +1.08879304, +1.98557353, +1.72576928, +1.93555689, +1.96572244, +1.08604622, +1.11490166, +1.38643026, +1.63345003, +1.86020839, +1.91566658, +1.35931277, +1.56485033, +1.03504968, +1.41288996, +1.80873227, +1.70452118, +1.04213607, +1.82422221, +1.81036067, +1.43197811, +1.52939463, +1.82486105, +1.51023400, +1.95711052, +1.12798667, +1.24041891

466

467adat = getFFTR(getFFTF(data)) / size(data)

468adat

469+1.77872026, +1.99383712, +1.31840658, +1.15132093, +1.11332095, +1.67639220, +1.02044773, +1.96374726, +1.48225689, +1.33696508, +1.79447210, +1.36099946, +1.91646123, +1.68929052, +1.43697345, +1.14321661, +1.58884907, +1.60564375, +1.27022612, +1.95489478, +1.14600563, +1.48850727, +1.23601031, +1.90985656, +1.92535889, +1.93595159, +1.91236341, +1.43223047, +1.09946072, +1.29791546, +1.61555064, +1.37773633, +1.61022961, +1.25531316, +1.75815868, +1.49250793, +1.10163319, +1.08879316, +1.98557353, +1.72576928, +1.93555689, +1.96572232, +1.08604634, +1.11490166, +1.38643026, +1.63345003, +1.86020863, +1.91566634, +1.35931301, +1.56485033, +1.03504980, +1.41288972, +1.80873227, +1.70452118, +1.04213619, +1.82422233, +1.81036079, +1.43197811, +1.52939475, +1.82486105, +1.51023400, +1.95711040, +1.12798679, +1.24041891

470reltol = sqrt(epsilon(1._TKG))

471reltol

472+0.345266977E-3

473isClose(data, adat, reltol = reltol)

474T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

475call setAsserted(all(isClose(data, adat, reltol = reltol)))

476

477lenData = getUnifRand(5, 100)

478lenData

479+66

480data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

481data

482+1.1542601008262605, +1.6799794341481635, +1.0715326035297272, +1.1314441527816723, +1.1067769924134452, +1.3773534883655776, +1.1061447350128879, +1.0319570584840703, +1.5841748171113754, +1.3278007547748221, +1.4516569817720621, +1.4315394689252978, +1.1320412088193037, +1.3236844691390937, +1.8527634794053296, +1.9004513898270146, +1.2574628682094353, +1.9093250767772461, +1.5583488059022810, +1.7105125809118129, +1.7142601016922954, +1.7887017247975681, +1.6864184414000873, +1.8267585723665116, +1.3664735024593408, +1.7446946406732342, +1.1698743611617557, +1.9423520038593649, +1.3385528078654647, +1.5017139413148224, +1.6104612567938692, +1.6954703068172947, +1.5130187198363925, +1.3846515794617185, +1.4832249502630126, +1.8981644211945672, +1.4289477997509432, +1.9183500649186789, +1.2589700630203391, +1.9072289543589127, +1.0584479845019432, +1.3697702480466414, +1.9021768940914456, +1.4934906691759795, +1.1512257671952235, +1.8949871439936619, +1.4466388967817929, +1.0314569105886808, +1.1370353005232310, +1.3013918176932586, +1.5066469847740191, +1.4059649367862770, +1.2367662428886641, +1.8163673564630769, +1.7207270295022532, +1.2895983153513195, +1.2573552606002243, +1.0035437151573274, +1.4681361656968703, +1.6882232007038165, +1.8637732457542220, +1.5104984975528506, +1.4248572311375942, +1.7361161093803745, +1.4686043351362623, +1.0214372312706774

483

484adat = getFFTR(getFFTF(data)) / size(data)

485adat

486+1.1542601008262607, +1.6799794341481638, +1.0715326035297277, +1.1314441527816723, +1.1067769924134456, +1.3773534883655778, +1.1061447350128875, +1.0319570584840700, +1.5841748171113752, +1.3278007547748221, +1.4516569817720621, +1.4315394689252978, +1.1320412088193041, +1.3236844691390934, +1.8527634794053294, +1.9004513898270150, +1.2574628682094358, +1.9093250767772463, +1.5583488059022810, +1.7105125809118127, +1.7142601016922951, +1.7887017247975681, +1.6864184414000871, +1.8267585723665114, +1.3664735024593411, +1.7446946406732340, +1.1698743611617561, +1.9423520038593651, +1.3385528078654649, +1.5017139413148231, +1.6104612567938688, +1.6954703068172938, +1.5130187198363916, +1.3846515794617176, +1.4832249502630119, +1.8981644211945661, +1.4289477997509428, +1.9183500649186775, +1.2589700630203384, +1.9072289543589118, +1.0584479845019426, +1.3697702480466400, +1.9021768940914456, +1.4934906691759793, +1.1512257671952240, +1.8949871439936621, +1.4466388967817929, +1.0314569105886817, +1.1370353005232310, +1.3013918176932584, +1.5066469847740187, +1.4059649367862770, +1.2367662428886641, +1.8163673564630762, +1.7207270295022532, +1.2895983153513193, +1.2573552606002245, +1.0035437151573279, +1.4681361656968708, +1.6882232007038167, +1.8637732457542218, +1.5104984975528502, +1.4248572311375940, +1.7361161093803743, +1.4686043351362623, +1.0214372312706776

487reltol = sqrt(epsilon(1._TKG))

488reltol

489+0.14901161193847656E-7

490isClose(data, adat, reltol = reltol)

491T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

492call setAsserted(all(isClose(data, adat, reltol = reltol)))

493

494lenData = getUnifRand(5, 100)

495lenData

496+72

497data = 1._TKG + getUnifRand(0._TKG, 1._TKG, lenData)

498data

499+1.19099665916960304631344013140468123, +1.82800107307093495186446930614092100, +1.61903130333806198075237926506220433, +1.69475728487438281642028772267302585, +1.48470539680893043740966434000657925, +1.85585029774028419967687228453420084, +1.53447068111392436109268828600507931, +1.73401093406159755181069608261490138, +1.19466611494793345550180650103407576, +1.55039731617101474977583798345523586, +1.50445830956335503579258730179407449, +1.39900840229682897537881462156147758, +1.95553364571173017455403990259649640, +1.18832112538342294299799642415956604, +1.21452439018100326336902295000771128, +1.22350060520511347052440679743659892, +1.82949785538380449443304706945939779, +1.54023775137316284348251550915206074, +1.84592073936688039709255831508205888, +1.93532050989273612283542027540011244, +1.10298601391300215410864475705489751, +1.71384400529705889431685502419258118, +1.12082826121105830051211416137961260, +1.78254628762620278835178132022850931, +1.48845700911041287764390216489989960, +1.34423113184225572318281605989374776, +1.37345992676752743056284203043853590, +1.30079201889922155737823465648078766, +1.38527421631067860702998557894620371, +1.40863210828394329236960736475633838, +1.85936857751973458252050981875254710, +1.37439272534946421794963781961354988, +1.18645064888063376326740652826336653, +1.68174449710955696639491290909325522, +1.48394980547663817998216567323385330, +1.29256522864512549465504935355715136, +1.11887996851196585859321190964725511, +1.06003698810345758950933908596097024, +1.08545687886097070644458770328958635, +1.82141468784533480443348018567981476, +1.96791005729675253597732175709020417, +1.71124339010385526658881783348819671, +1.66772994340399915852513162337025220, +1.72879031215892554078985777763762967, +1.38202353434010355567209708522522888, +1.38485944229602553014225485447718260, +1.00628231120968737487337080491376460, +1.11834885561118338931049941406601623, +1.24329722837992409654177995671826642, +1.76860354116594120030029054927860540, +1.75292927036946420896912402136448554, +1.20795150731564521274595546524778525, +1.67939051648500926618595517387765225, +1.44982570551187560299794747790297088, +1.65736525673402819792390574376702308, +1.00406495478588179616101914375428564, +1.06951429557356693454060424261678016, +1.54373720600542171976532802259427470, +1.47738393946260953888123455664701108, +1.11666083915155154711020924634268058, +1.59537249782009262518133165376753533, +1.86952376362023625238591852595942716, +1.35683830933270857318076852804607963, +1.88545009139501769501865645665712420, +1.23973068417036849956805550200427566, +1.78070724066283803893027649285760404, +1.43584864641788076954777210122349386, +1.48931744236446517180204659006897141, +1.17949406986255706972717546834889523, +1.61856460341130629735636550902033227, +1.19032196516113220068699101686720374, +1.81025548289900439335600860061880284

500

501adat = getFFTR(getFFTF(data)) / size(data)

502adat

503+1.19099665916960304631344013140468104, +1.82800107307093495186446930614092139, +1.61903130333806198075237926506220452, +1.69475728487438281642028772267302623, +1.48470539680893043740966434000657886, +1.85585029774028419967687228453420104, +1.53447068111392436109268828600507970, +1.73401093406159755181069608261490177, +1.19466611494793345550180650103407557, +1.55039731617101474977583798345523624, +1.50445830956335503579258730179407468, +1.39900840229682897537881462156147777, +1.95553364571173017455403990259649582, +1.18832112538342294299799642415956623, +1.21452439018100326336902295000771166, +1.22350060520511347052440679743659892, +1.82949785538380449443304706945939779, +1.54023775137316284348251550915206112, +1.84592073936688039709255831508205907, +1.93532050989273612283542027540011225, +1.10298601391300215410864475705489732, +1.71384400529705889431685502419258118, +1.12082826121105830051211416137961279, +1.78254628762620278835178132022850931, +1.48845700911041287764390216489989921, +1.34423113184225572318281605989374776, +1.37345992676752743056284203043853629, +1.30079201889922155737823465648078785, +1.38527421631067860702998557894620351, +1.40863210828394329236960736475633838, +1.85936857751973458252050981875254729, +1.37439272534946421794963781961354988, +1.18645064888063376326740652826336653, +1.68174449710955696639491290909325541, +1.48394980547663817998216567323385349, +1.29256522864512549465504935355715136, +1.11887996851196585859321190964725491, +1.06003698810345758950933908596097062, +1.08545687886097070644458770328958673, +1.82141468784533480443348018567981496, +1.96791005729675253597732175709020398, +1.71124339010385526658881783348819690, +1.66772994340399915852513162337025239, +1.72879031215892554078985777763762948, +1.38202353434010355567209708522522869, +1.38485944229602553014225485447718279, +1.00628231120968737487337080491376479, +1.11834885561118338931049941406601643, +1.24329722837992409654177995671826604, +1.76860354116594120030029054927860520, +1.75292927036946420896912402136448592, +1.20795150731564521274595546524778564, +1.67939051648500926618595517387765225, +1.44982570551187560299794747790297088, +1.65736525673402819792390574376702327, +1.00406495478588179616101914375428584, +1.06951429557356693454060424261678016, +1.54373720600542171976532802259427489, +1.47738393946260953888123455664701128, +1.11666083915155154711020924634268058, +1.59537249782009262518133165376753495, +1.86952376362023625238591852595942716, +1.35683830933270857318076852804607982, +1.88545009139501769501865645665712420, +1.23973068417036849956805550200427566, +1.78070724066283803893027649285760424, +1.43584864641788076954777210122349424, +1.48931744236446517180204659006897141, +1.17949406986255706972717546834889504, +1.61856460341130629735636550902033246, +1.19032196516113220068699101686720393, +1.81025548289900439335600860061880304

504reltol = sqrt(epsilon(1._TKG))

505reltol

506+0.138777878078144567552953958511352539E-16

507isClose(data, adat, reltol = reltol)

508T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T, T

509call setAsserted(all(isClose(data, adat, reltol = reltol)))

510

511

Test:: test_pm_fftpack

Final Remarks ⛓

If you believe this algorithm or its documentation can be improved, we appreciate your contribution and help to edit this page's documentation and source file on GitHub.
For details on the naming abbreviations, see this page.
For details on the naming conventions, see this page.
This software is distributed under the MIT license with additional terms outlined below.

If you use any parts or concepts from this library to any extent, please acknowledge the usage by citing the relevant publications of the ParaMonte library.
If you regenerate any parts/ideas from this library in a programming environment other than those currently supported by this ParaMonte library (i.e., other than C, C++, Fortran, MATLAB, Python, R), please also ask the end users to cite this original ParaMonte library.

This software is available to the public under a highly permissive license.
Help us justify its continued development and maintenance by acknowledging its benefit to society, distributing it, and contributing to it.

Copyright: Computational Data Science Lab

Author:: Fatemeh Bagheri, Tuesday 11:34 PM, August 10, 2021, Dallas, TX

Definition at line 1156 of file pm_fftpack.F90.

The documentation for this interface was generated from the following file:

src/fortran/main/pm_fftpack.F90